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241 results on '"Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord"'

1. Analysis of the Rolling Carpet Strategy to Eradicate an Invasive Species

Author: Luis Almeida, Alexis Léculier, Nicolas Vauchelet, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, European Project: 740623,H2020 Pilier ERC,ADORA(2017), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Comparison principle, Population dynamics, comparison principle AMS subject classifications: 35K57, Applied Mathematics, Reaction-diusion equations, 35C07, 92D25, Computational Mathematics, Mathematics - Analysis of PDEs, Reaction-diffusion equations, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], comparison principle AMS subject classications: 35K57, AMS subject classifications: 35K57, 92D25, 35C07, Analysis, Analysis of PDEs (math.AP)
Abstract: International audience; In order to prevent the propagation of human diseases transmitted by mosquitoes (such as dengue or zika), one possible solution is to act directly on the mosquito population. In this work, we consider an invasive species (the mosquitoes) and we study two strategies to eradicate the population in the whole space by a local intervention. The dynamics of the population is modeled through a bistable reaction diffusion equation in an one dimensional setting and both strategies are based on the same idea : we act on a moving interval. The action of the first strategy is to kill as many individuals as we can in this moving interval. The action of the second strategy is to release sterile males in this moving interval. For both strategies, we manage to generate traveling waves that propagate in the opposite direction relative to the one of the natural invasive traveling wave. These cases correspond to succeeding in eradicating the invasive species. Furthermore, for the first strategy, we fully characterize the minimal size of the interval. All the results are illustrated by numerical simulations.
Published: 2023

2. DISCRETE-TIME ANALYSIS OF OPTIMIZED SCHWARZ WAVEFORM RELAXATION WITH ROBIN PARAMETERSDEPENDING ON THE TARGETED ITERATION COUNT

Author: Arnoult, Arthur, Japhet, Caroline, Omnes, Pascal, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Subjects: Iteration-dependent Robin parameters, Robin transmission conditions, Optimized Schwarz waveform relaxation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete-time convergence analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We propose a new approach to analyze the convergence of optimized Schwarz waveform relaxation (OSWR) iterations for parabolic problems. Departing from traditional Fourier analysis in the time direction, we explicitly solve the equations obtained using the backward Euler scheme in time, and deduce convergence properties from this solution, in the two subdomains case. Convergence is proven for any positive Robin parameter (or couple of such parameters in the two-sided case). We also show that, for any fixed value of the number of time steps, the convergence depends on a single parameter which is a combination of the diffusion coefficient, the time step and the Robin parameter. A convergence result in a finite number of iterations is also proven for a well-chosen value of the Robin parameters. This approach allows us to define efficient optimized Robin parameters that depend on the number of iterations one wishes to perform, and to recommend a couple (number of iterations, Robin parameter) to reach a given accuracy. Numerical experiments illustrate the performance of such iteration-dependent optimized Robin parameters, compared to the observed optimal ones (which also depend on the number of iterations performed). A comparison is also given with optimized parameters derived by classical Fourier transform analysis on the continuous problem (which are independent of the iterations).
Published: 2023

3. OPTIMIZED SCHWARZ WAVEFORM RELAXATION METHOD FOR INCOMPRESSIBLE STOKES PROBLEM *

Author: Bui, Duc-Quang, Japhet, Caroline, Omnes, Pascal, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Service de Génie Logiciel pour la Simulation (SGLS), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, and ANR-15-CE23-0019,CINE-PARA,Méthodes de parallélisation pour cinétiques complexes(2015)
Subjects: correction technique for the pressure, 65M55, 35K45, 76D07, 65M12, 65M22, 65B99, optimized Schwarz waveform relaxation, Unsteady incompressible Stokes system, Robin transmission conditions, space-time domain decomposition, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: We propose and analyse the optimized Schwarz waveform relaxation (OSWR) method for the unsteady incompressible Stokes equations. Well-posedness of the local subdomain problems with Robin boundary conditions is proved. Convergence of the velocity is shown through energy estimates; however, pressure converges only up to constant values in the subdomains, and an astute correction technique is proposed to recover these constants from the velocity. The convergence factor of the OSWR algorithm is obtained through a Fourier analysis, and allows to efficiently optimize the space-time Robin transmission conditions involved in the OSWR method. Then, numerical illustrations for the two-dimensional unsteady incompressible Stokes system are presented to illustrate the performance of the OSWR algorithm.
Published: 2023

4. A posteriori error estimates for the large eddy simulation applied to incompressible fluids

Author: Nassreddine, Ghina, Omnes, Pascal, Sayah, Toni, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Saint-Joseph de Beyrouth (USJ), Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Subjects: a posteriori estimation, finite element method, Large Eddy Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: We study the two dimensional time dependent Large Eddy Simulation method applied to the incompressible Navier-Stokes system with Smagorinsky’s eddy viscosity model and a filter width that depends on the local mesh size. The discrete model is based on the implicit Euler scheme and a conforming finite element method for the time and space discretizations, respectively. We establish a reliable and efficient a posteriori error estimation between the numerical LES solution and the exact solution of the original Navier-Stokes system, which involves three types of error indicators respectively related to the filter and to the discretizations in time and space. Numerical results show the effectiveness of adaptive simulations.
Published: 2023

5. Generic representations of finite general linear groups in cross characteristic

Author: Djament, Aurélien, Gaujal, Thomas, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), ANR-16-CE40-0003,ChroK,Homotopie chromatique et K-théorie(2016), ANR-19-CE40-0001,AlMaRe,Aspects algébriques des groupes de difféotopie et de groupes s'y rattachant(2019), and ANR-11-LABX-0007,CEMPI,Centre Européen pour les Mathématiques, la Physique et leurs Interactions(2011)
Subjects: [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], catégories de foncteurs, recollements de catégories abéliennes, simple functors, catégories additives, recollements of abelian categories, additive categories, foncteurs antipolynomiaux, foncteurs simples, antipolynomial functors, MSC2020 : 8A25, 18E05, 18E10, 18E35, 19A99, 20G99, 20J99, [MATH.MATH-KT]Mathematics [math]/K-Theory and Homology [math.KT], functor categories, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Abstract: We study generic representations of general linear groups over a finite ring R with coefficients in a field k in which the cardinality of R is invertible, that is functors from finitely-generated projective R-modules to k-vector spaces. We obtain especially a classification of such simple representations, what allows to prove a conjecture of Djament-Touzé-Vespa on dimensions taken by such a functor.; On étudie les représentations génériques des groupes linéaires sur un anneau fini R à coefficients dans un corps k dans lequel le cardinal de R est inversible, c'est-à-dire les foncteurs depuis les R-modules projectifs de type fini vers les k-espaces vectoriels. On obtient en particulier une classification de ces représentations simples qui permet de démontrer une conjecture de Djament-Touzé-Vespa sur les dimensions prises par un tel foncteur.
Published: 2023

6. A control strategy for Sterile Insect Techniques using exponentially decreasing releases to avoid the hair-trigger effect

Author: Léculier, Alexis, Nguyen, Nga, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Université de Bordeaux (UB), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), The ﬁrst author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 740623).The second author has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement No 945322., and European Project: 740623,H2020 Pilier ERC,ADORA(2017)
Subjects: hair-trigger effect, traveling waves, Mathematics - Analysis of PDEs, sterile insect technique hair-trigger effect traveling waves, [SDV.BID.EVO]Life Sciences [q-bio]/Biodiversity/Populations and Evolution [q-bio.PE], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], sterile insect technique, Analysis of PDEs (math.AP)
Abstract: In this paper, we introduce a control strategy for applying the Sterile Insect Technique (SIT) to eliminate the population of Aedes mosquitoes which are vectors of various deadly diseases like dengue, zika, chikungunya... in a wide area. We use a system of reaction-diffusion equations to model the mosquito population and study the effect of releasing sterile males. Without any human intervention, and due to the so-called hair-trigger effect, the introduction of only a few individuals (eggs or fertilized females) can lead to the invasion of mosquitoes in the whole region after some time. To avoid this phenomenon, our strategy is to keep releasing a small number of sterile males in the treated zone and move this release forward with a negative forcing speed c to push back the invasive front of wild mosquitoes. By using traveling wave analysis, we show in the present paper that the strategy succeeds in repulsing the population while consuming a finite amount of mosquitoes in any finite time interval even though we treat a moving half-space {x > ct}. Moreover, we succeed in constructing a 'forced' traveling wave for our system moving at the same speed as the releases. We also provide some numerical illustrations for our results.
Published: 2023

7. Non-Triangular Self-Synchronizing Stream Ciphers

Author: Philippe Guillot, Marine Minier, Paul Huynh, Julien Francq, Loic Besson, Gilles Millérioux, Airbus CyberSecurity SAS [Élancourt], Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Cryptology, arithmetic : algebraic methods for better algorithms (CARAMBA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), This work was partially supported by the French National Agency of Research under the grants number ANR-13-INSE-0005-01 and by the french PIA project 'Lorraine Université d’Excellence', reference ANR-15-IDEX-04-LUE., IMPACT-DIGITRUST, ANR-15-IDEX-0004,LUE,Isite LUE(2015), ANR-13-INSE-0005,THE CASCADE,THEorie du Contrôle Appliquée à la Synchronisation des CommunicAtions DiscrEtes(2013), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Finite-state machine, Dynamical systems theory, business.industry, Computer science, stream ciphers, Synchronizing, Topology, control theory, Theoretical Computer Science, Automaton, symmetric cryptography, Computational Theory and Mathematics, Symmetric-key algorithm, Hardware and Architecture, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, finite state automata, business, Representation (mathematics), Stream cipher, Software
Abstract: International audience; In this paper, we propose an instantiation, called \textsf{Stanislas}, of a dedicated Self-Synchronizing Stream Cipher (SSSC) involving an automaton with finite input memory using non-triangular state transition functions. Previous existing SSSC are based on automata with shifts or triangular functions (T-functions) as state transition functions. Our algorithm Stanislas admits a matrix representation deduced from a general and systematic methodology called Linear Parameter Varying (LPV). This particular representation comes from the automatic theory and from a special property of dynamical systems called flatness.
Published: 2022

8. Actions de membranes pour les ∞-opérades cohérentes

Author: Pourcelot, Hugo, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Sorbonne Paris Nord, Université Paris 13 (UP13), and European Project
Subjects: operad, topological field theories, twisted arrows, [MATH.MATH-AT]Mathematics [math]/Algebraic Topology [math.AT], higher category theory, coherent ∞-operads, Brane action, string and brane topology, cospans, little disks operad, marked simplicial sets, [MATH.MATH-CT]Mathematics [math]/Category Theory [math.CT]
Abstract: 59 pages; We prove that Mann-Robalo's construction of the brane action extends to general coherent ∞-operads, with possibly multiple colors and non-contractible spaces of unary operations. This requires to establish two results regarding spaces of extensions that were left unproven in the aforementioned construction. First, we show that Lurie's and Mann-Robalo's models for such spaces are equivalent. Second, we prove that the space of extensions in the sense of Lurie is not in general equivalent to the homotopy fiber of the associated forgetful morphism, but rather to its homotopy quotient by the ∞-groupoid of unary operations, correcting an oversight in existing literature. As an application, we obtain that the ∞-operads of B-framed little disks are coherent and therefore yield new operations on spaces of branes of perfect derived stacks.; On montre que la construction par Mann-Robalo de l'action de membranes s'étend aux ∞-opérades cohérentes générales, colorées et d'espaces d'opérations unaires non-contractiles. Cela requiert d'établir deux résultats concernant les espaces d'extensions laissés sans preuve dans la construction précédente. Le premier établit l'équivalence entre les modèles de Lurie et de Mann-Robalo pour ces espaces. Au travers du second résultat, on montre que l'espaces des extensions au sens de Lurie n'est en général pas équivalent à la fibre homotopique du morphisme d'oubli associé, mais au contraire s'identifie à son quotient homotopique par l'action naturelle de l'∞-groupoïde des opérations unaires, corrigeant ainsi une erreur de la littérature existante. Finalement, on applique les résultats précédents pour démontrer la cohérence des ∞-opérades de petits disques à repères B-tordus, ce qui donne des nouvelles opérations sur les espaces de membranes des champs dérivés parfaits.
Published: 2023

9. The Massey vanishing conjecture for number fields

Author: Harpaz, Yonatan, Wittenberg, Olivier, Wittenberg, Olivier, Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Laboratoire de Mathématiques d'Orsay (LMO), and Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematics - Algebraic Geometry, Mathematics - Number Theory, Mathematics::Number Theory, General Mathematics, FOS: Mathematics, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Number Theory (math.NT), Algebraic Geometry (math.AG), Mathematics::Algebraic Topology, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Abstract: A conjecture of Min\'a\v{c} and T\^an predicts that for any n>2, any prime p and any field k, the Massey product of n Galois cohomology classes in H^1(k,Z/pZ) must vanish if it is defined. We establish this conjecture when k is a number field., Comment: 33 pages; improved exposition, final version
Published: 2023

10. Investigating the effect of process parameters for fused filament fabrication

Author: Asma Boumedine, Samir Lecheb, Khaled Benfriha, Pascal Omnes, Laboratoire Conception de Produits et Innovation (LCPI), Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), Université M'Hamed Bougara Boumerdes (UMBB), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Design of experiment (DOE), Mathematical modelling, Additive manufacturing, Génie des procédés [Sciences de l'ingénieur], Full factorial design, Dimensional accuracy, [SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering, Fused Filament Fabrication (FFF), Geometrical characterization, Industrial and Manufacturing Engineering, Composites
Abstract: International audience; Fused Filament Fabrication (FFF) is a promising technology that is largely developed in small series, as this technology optimizes supply chains by reducing production time and costs. However, its shortcomings have slowed its adoption as a dominant production technology. Among its weaknesses, this work focuses on geometric and dimensional accuracy within tolerance range. There is a need for understanding the sources of geometrical inaccuracies and for methods of characterizing them, in order to modify the input parameters to eventually obtain the desired geometry. This work first focuses on the geometric and dimensional accuracy of parts printed by the FFF process by studying the influence of the inner radius of a cylindrical part, the type of material and the type of filling pattern. The levels with the greatest dimensional dispersion are the largest radius, the nylon material, and the hexagonal filling pattern. Secondly, a defect characterization method associated with a parametric mathematical model is developed. The 3D scanner enables the retrieval of the coordinates of the printed geometry; this allows to characterize the errors with respect to the theoretical 3D model and to modelize the printed part by a series of ellipses of which we obtain the analytical equations, as a first step of a correction process.
Published: 2023

11. Analysis of dissipation operators that damp spurious modes while maintaining discrete approximate geostrophic equilibriums for the B-grid staggered scheme on triangular meshes

Author: Do, Minh-Hieu, Nguyen, Van-Thanh, Omnes, Pascal, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Subjects: [PHYS]Physics [physics], Shallow water equation with Coriolis source term, [MATH]Mathematics [math], Spurious mode damping, geostrophic equilibrium, Low Froude number, Hodge decomposition, Staggered schemes, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We consider the lowest order - so called B-grid - discretization on triangular cells which is common in the ocean or atmosphere simulation science, with pressure field at the vertices of the triangles and the velocity field at the cell centers. It is known that this discretization presents spurious modes due to a too large number of velocities unknowns and that these modes should be damped; since preservation of approximate geostrophic equilibrium (GE) may be of primary importance in the simulations, we propose and analyze damping operators that, when applied to the linearized constant coefficient configuration, exactly preserve discrete versions of the GEs. We also analyze their effects in more general configurations and their possible coupling with more standard damping operators. These strategies cover triangular variants of the Low Froude (LF) scheme [1], the Apparent Topography (AT) scheme [2, 3], as well as a new modification of it. The LF scheme has no numerical diffusion terms in the pressure equation and damps the normal velocity jumps between adjacent cells in the momentum equation. In the AT scheme, numerical diffusion is added in the pressure equation in such a way that it does not impact the discrete GE. However, since the AT scheme alone cannot be proved to be damping through energy estimates and does not preserve the space which is orthogonal to the discrete GE, we also study what we call the Modified Apparent Topography (MAT) that satisfies these important properties. We also suggest semi-implicit time discretizations that preserve these properties. Extensions to the full non-linear equations are also provided. Numerical experiments illustrate the performance of the new schemes.
Published: 2023

12. Prismatic Dieudonné theory

Author: Johannes Anschütz, Arthur-César Le Bras, Le Bras, Arthur-César, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Statistics and Probability, Algebra and Number Theory, [MATH] Mathematics [math], Computer Science::Robotics, Mathematics::K-Theory and Homology, Mathematics::Category Theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology, Number Theory (math.NT), [MATH]Mathematics [math], Algebraic Geometry (math.AG), Mathematical Physics, Analysis
Abstract: We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $\mathrm{DM}^{\rm adm}(R)$ of \textit{admissible prismatic Dieudonné crystals over $R$} and a natural functor from $p$-divisible groups over $R$ to $\mathrm{DM}^{\rm adm}(R)$. We prove that this functor is an antiequivalence. Our main cohomological tool is the prismatic formalism recently developed by Bhatt and Scholze., Replaced the notion of filtered prismatic Dieudonn\'e crystal by the equivalent (but simpler) notion of admissible prismatic Dieudonn\'e crystal; corrected and simplified (following a suggestion of Mathew) the proof of fully faithfulness; many small changes
Published: 2023

13. Prise en compte de la topographie dans un modèle de Saint-Venant à deux vitesses : solutions stationnaires et schémas numériques

Author: Boulos Al Makary, Nelly, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sorbonne Paris Nord, Emmanuel Audusse, Nina Aguillon, and Martin Parisot
Subjects: Volumes finis, Topography, Steady state solutions, Supercritique, Schéma à l'équilibre, Topographie, Solutions stationnaires, Riemann problem, Système de Saint Venant à deux vitesses, Subcritique, Subcritical flow, Discontinuities, Well-balanced schemes, Shallow water model with two velocities, Supercritical flow, Transcritique, Discontinuité, [MATH]Mathematics [math], Finite volume
Abstract: In this work, we are interested in the analysis of the "Shallow water model with two velocities".First, we study the steady state solutions using the Bernouilli's principle for $C^1$ regular solutions and the Rankine-Hugoniot relations through discontinuities. Then, we present the types of solutions, their existence and their uniqueness depending on the boundary conditions.Second, we propose several finite volume approximate Riemann solvers for the resolution of the homogeneous Shallow water model with two velocities. The construction of the schemes is based on a recent analysis of the Riemann problem. We present several test cases to illustrate the behavior and the properties of the schemes.Afterwards, we extend these schemes for the model with topography and we propose a suitable numerical approximation of the source term. We prove that the proposed schemes are well-balanced and ensure the positivity of the water heights.Finally, we study the numerical stability of the stationary solutions.; L'objectif de ce travail est d'étudier les solutions stationnaires du modèle de Saint Venant à deux vitesses et ensuite de développer des solveurs de Riemann dits "well-balanced" ou équilibre capables de préserver toute solution stationnaire régulière en 1D sous une topographie arbitraire continue.Dans ce but, nous analysons dans un premier temps les solutions stationnaires. Ensuite, nous proposons des solveurs de Riemann pour le système homogène à deux vitesses, i.e sans topographie. Par la suite, nous étendons ces schémas pour prendre en considération le présence de la topographie. Nous validons les différentes parties de notre étude par des résultats numériques.
Published: 2022

14. How to find a discrete entropy inequality when you don’t know if it exists

Author: Aguillon, Nina, Audusse, Emmanuel, Desveaux, Vivien, Salomon, Julien, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université de Picardie Jules Verne (UPJV), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 (LAMFA), and Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS)
Subjects: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: The solutions of hyperbolic systems contain discontinuities. These weak solutions verify not only the original PDEs, but also an entropy inequality that acts as a selection criterion determining whether a discontinuity is physical or not. Obtaining a discrete version of these entropy inequalities when approximating the solutions numerically is crucial to avoid convergence to unphysical solutions or even unstability. In this paper, we introduce an optimization framework that enable to quantify a posteriori entropy. We use it to obtain maps of numerical diffusion and to prove that some schemes do not have a discrete entropy inequality.
Published: 2022

15. Ruelle–Pollicott resonances for manifolds with hyperbolic cusps

Author: Tobias Weich, Yannick Guedes Bonthonneau, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, and Universität Paderborn (UPB)
Subjects: Mathematics::Dynamical Systems, Applied Mathematics, General Mathematics, 010102 general mathematics, Spectrum (functional analysis), Mathematics::Geometric Topology, 01 natural sciences, Nonlinear Sciences::Chaotic Dynamics, 0103 physical sciences, Geodesic flow, Mathematics::Differential Geometry, 010307 mathematical physics, Negative curvature, 0101 mathematics, Finite set, ComputingMilieux_MISCELLANEOUS, [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP], Mathematics, Mathematical physics
Abstract: We present new methods to construct a Ruelle-Pollicott spectrum for the geodesic flow on manifolds with strictly negative curvature and a finite number of hyperbolic cusps.
Published: 2021

16. A posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation

Author: Dakroub, Jad, Faddoul, Joanna, Omnes, Pascal, Sayah, Toni, Université Saint-Joseph de Beyrouth (USJ), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Paris 8 Vincennes-Saint-Denis (UP8)-Université Paris 13 (UP13)-Institut Galilée-Centre National de la Recherche Scientifique (CNRS), Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Subjects: Navier-Stokes problem, A posteriori error estimation, finite element method, adaptive methods, convection-diffusion-reaction equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this paper we study the a posteriori error estimates for the time dependent Navier-Stokes system coupled with the convection-diffusion-reaction equation. The problem is discretized in time using the implicit Euler method and in space using the finite element method. We establish a posteriori error estimates with two types of computable error indicators, the first one linked to the space discretization and the second one to the time discretization. Finally, numerical investigations are performed and presented.
Published: 2022

17. Utilisation des assistants de preuves pourl’enseignement en L1

Author: Kerjean, Marie, Le Roux, Frédéric, Massot, Patrick, Mayero, Micaela, Mesnil, Zoé, Modeste, Simon, Narboux, Julien, Rousselin, Pierre, Laboratoire d'Informatique de Paris-Nord (LIPN), Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Faculté des Sciences d’Orsay, Université Paris-Saclay, 91405 Orsay Cedex, France., Laboratoire de Didactique André Revuz (LDAR (URP_4434)), Université de Rouen Normandie (UNIROUEN), Normandie Université (NU)-Normandie Université (NU)-Université de Lille-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Université Paris Cité (UPCité)-CY Cergy Paris Université (CY), Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Sorbonne Paris Nord, and Narboux, Julien
Subjects: [MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM], [INFO.EIAH] Computer Science [cs]/Technology for Human Learning, proof, proving, assistant de preuve, enseignement de la démonstration, [MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM], [INFO.EIAH]Computer Science [cs]/Technology for Human Learning, Proof assistant, teaching
Abstract: National audience; Utilisation des assistants de preuves pour l'enseignement en L1 Utilisation des assistants de preuves pour l'enseignement en L1 Retours d'expériences Nous rendons compte de cinq expériences récentes de l'enseignement de la démonstration utilisant les assistants de preuve Coq, D∃∀DUCTION, Edukera et Lean.
Published: 2022

18. The Field Q and the Equality 0.999 . . . = 1 from Combinatorics of Circular Words and History of Practical Arithmetics

Author: Rittaud, Benoît, Vivier, Laurent, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Laboratoire de Didactique André Revuz (LDAR (EA_4434)), Université d'Artois (UA)-Université Paris Diderot - Paris 7 (UPD7)-Université de Cergy Pontoise (UCP), Université Paris-Seine-Université Paris-Seine-Université de Rouen Normandie (UNIROUEN), and Normandie Université (NU)-Normandie Université (NU)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)
Subjects: History and Overview (math.HO), [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], Mathematics - History and Overview, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract: We reconsider the classical equality 0.999. .. = 1 with the tool of circular words, that is: finite words whose last letter is assumed to be followed by the first one. Such circular words are naturally embedded with algebraic structures that enlight this problematic equality, allowing it to be considered in Q rather than in R. We comment early history of such structures, that involves English teachers and accountants of the first part of the xviii th century, who appear to be the firsts to assert the equality 0.999. .. = 1. Their level of understanding show links with Dubinsky et al.'s apos theory in mathematics education. Eventually, we rebuilt the field Q from circular words, and provide an original proof of the fact that an algebraic integer is either an integer or an irrational number.
Published: 2022

19. Steady-state solutions for a reaction-diffusion equation with Robin boundary conditions: Application to the control of dengue vectors

Author: Almeida, Luís, Bliman, Pierre-Alexandre, Nguyen, Nga, Vauchelet, Nicolas, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: robin boundary conditions, Mathematics - Analysis of PDEs, Reaction-diffusion equations, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], steady-state solutions, Analysis of PDEs (math.AP)
Abstract: In this paper, we investigate an initial-boundary-value problem of a reaction-diffusion equation in a bounded domain with a Robin boundary condition and introduce some particular parameters to consider the non-zero flux on the boundary. This problem arises in the study of mosquito populations under the intervention of the population replacement method, where the boundary condition takes into account the inflow and outflow of individuals through the boundary. Using phase-plane analysis, the present paper studies the existence and properties of non-constant steady-state solutions depending on several parameters. Then, we use the principle of linearized stability to prove some sufficient conditions for their stability. We show that the long-time efficiency of this control method depends strongly on the size of the treated zone and the migration rate. To illustrate these theoretical results, we provide some numerical simulations in the framework of mosquito population control.
Published: 2022

20. Friction mediated by transient elastic linkages: extension to loads of bounded variation

Author: Allouch, Samar, Milišić, Vuk, Université Sorbonne Paris Nord - UFR des Sciences de la communication (USPN UP13 UFR SC), Université Sorbonne Paris Nord, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Laboratoire de Mathématiques de Bretagne Atlantique (LMBA), Université de Bretagne Sud (UBS)-Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), and Université de Brest (UBO)
Subjects: Numerical Analysis, Applied Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: In this work, we are interested in the convergence of a system of integro-differential equations with respect to an asymptotic parameter ε. It appears in the context of cell adhesion modelling [16, 15]. We extend the framework from [12, 13], strongly depending on the hypothesis that the external load f is in Lip([0, T ]) to the case where f ∈ BV(0, T) only. We show how results presented in [13] naturally extend to this new setting, while only partial results can be obtained following the comparison principle introduced in [12].
Published: 2022

21. A posteriori error estimates for the large eddy simulation applied to stationary Navier–Stokes equations

Author: Pascal Omnes, Toni Sayah, Ghina Nassreddine, Université Saint-Joseph de Beyrouth (USJ), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay
Subjects: Numerical Analysis, Applied Mathematics, finite element method, Navier-Stokes, Large Eddy Simulation, Finite element method, a posteriori error estimation, Computational Mathematics, Applied mathematics, A priori and a posteriori, Navier stokes, Navier–Stokes equations, Analysis, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Large eddy simulation, Mathematics
Abstract: International audience; In this paper, we study in two and three space dimensions, the a posteriori error estimates for the Large Eddy Simulation applied to the Navier-Stokes system. We begin by introducing the Navier-Stokes and the corresponding Large Eddy Simulation (LES) equations. Then we introduce the corresponding discrete problem based on the finite element method. We establish an a posteriori error estimation with three types of error indicators related to the filter of the LES method, to the discretization and to the linearization. Finally, numerical investigations are shown and discussed.
Published: 2022

22. A posteriori error estimates for the time-dependent convection-diffusion-reaction equation coupled with the Darcy system

Author: Nancy Chalhoub, Rebecca El Zahlaniyeh, Toni Sayah, Pascal Omnes, Université Saint-Joseph de Beyrouth (USJ), Service de Thermo-hydraulique et de Mécanique des Fluides (STMF), Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: a posteriori error estimates, Discretization, Applied Mathematics, Numerical analysis, finite element method, Space (mathematics), Backward Euler method, convection-diffusion-reaction equation, Finite element method, Darcy–Weisbach equation, A priori and a posteriori, Applied mathematics, Darcy's equations, adaptive methods, Convection–diffusion equation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; In this article, we consider the time dependent convection-diffusion-reaction equation coupled with the Darcy equation. We propose a numerical scheme based on finite element methods for the discretization in space and the implicit Euler method for the discretization in time. We establish optimal a posteriori error estimates with two types of computable error indicators, the first one linked to the time discretization and the second one to the space discretization. Finally, numerical investigations are performed and presented.
Published: 2021

23. Central values of additive twists of Maa{\ss} forms $L$-functions

Author: Drappeau, Sary, Nordentoft, Asbjørn Christian, Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, IRN GANDA, IRN MaDeF, and Independent Research Fund Denmark DFF-1025-00020B
Subjects: Mathematics - Number Theory, 11F03, 11F67, 11K50, 60F05, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT]
Abstract: In the present paper we study the central values of additive twists of Maa{\ss} forms $L$-series. In the case of the modular group, we show that the additive twists (when averaged over denominators) are asymptotically normally distributed. This supplements the recent work of Petridis--Risager which settled an averaged version of a conjecture of Mazur--Rubin concerning modular symbols. The methods of the present paper combine dynamical input due to Bettin and the first named author with the new fact that the additive twists define quantum modular forms in the sense of Zagier. This latter property is shown for a general discrete, co-finite group with cusps. Our results also has a number of arithmetic applications; in the case of Hecke congruence groups the quantum modularity implies certain reciprocity relations for twisted moments of twisted ${\rm GL}_2$-automorphic $L$-functions, extending results of Conrey and the second named author. In the case of cuspidal Maa{\ss} forms for the modular group, we also obtain a calculation of certain wide moments of twists of the $L$-function of the Maa{\ss} form., Comment: 48 pages
Published: 2022

24. A further study of quadratic APN permutations in dimension nine

Author: Christof Beierle, Claude Carlet, Gregor Leander, Léo Perrin, Ruhr University Bochum (RUB), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, University of Bergen (UiB), Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ruhr University Bochum, Bochum, Germany., Université Paris 8, LAGA, and Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: FOS: Computer and information sciences, Algebra and Number Theory, EA-equivalence, Applied Mathematics, Information Theory (cs.IT), Computer Science - Information Theory, General Engineering, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], Theoretical Computer Science, CCZ-equivalence, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], APN permutations, Inﬁnite family, 06E30, 94A60, [MATH]Mathematics [math], Boolean functions
Abstract: Recently, Beierle and Leander found two new sporadic quadratic APN permutations in dimension 9. Up to EA-equivalence, we present a single trivariate representation of those two permutations as $C_u \colon (\mathbb{F}_{2^m})^3 \rightarrow (\mathbb{F}_{2^m})^3, (x,y,z) \mapsto (x^3+uy^2z, y^3+uxz^2,z^3+ux^2y)$, where $m=3$ and $u \in \mathbb{F}_{2^3}\setminus\{0,1\}$ such that the two permutations correspond to different choices of $u$. We then analyze the differential uniformity and the nonlinearity of $C_u$ in a more general case. In particular, for $m \geq 3$ being a multiple of 3 and $u \in \mathbb{F}_{2^m}$ not being a 7-th power, we show that the differential uniformity of $C_u$ is bounded above by 8, and that the linearity of $C_u$ is bounded above by $8^{1+\lfloor \frac{m}{2} \rfloor}$. Based on numerical experiments, we conjecture that $C_u$ is not APN if $m$ is greater than $3$. We also analyze the CCZ-equivalence classes of the quadratic APN permutations in dimension 9 known so far and derive a lower bound on the number of their EA-equivalence classes. We further show that the two sporadic APN permutations share an interesting similarity with Gold APN permutations in odd dimension divisible by 3, namely that a permutation EA-inequivalent to those sporadic APN permutations and their inverses can be obtained by just applying EA transformations and inversion to the original permutations.
Published: 2022

25. Analytic solutions of two problems of Biology and Physics using the Jacobi elliptic functions

Author: Dubois, François, Lafitte, Olivier, Poignard, Clair, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), International Research Lab (IRL CRM-CNRS), Centre de Recherches Mathématiques [Montréal] (CRM), Université de Montréal (UdeM)-Université de Montréal (UdeM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Modélisation Mathématique pour l'Oncologie (MONC), 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)-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)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre de recherches Mathématiques
Subjects: [PHYS]Physics [physics], [MATH]Mathematics [math]
Abstract: International audience
Published: 2022

26. Optimal Immunity Control and Final Size Minimization by Social Distancing for the SIR Epidemic Model

Author: Nicolas Vauchelet, Michel Duprez, Yannick Privat, Pierre-Alexandre Bliman, Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Computational Anatomy and Simulation for Medicine (MIMESIS), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie (ICube), École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)-Réseau nanophotonique et optique, Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-École Nationale du Génie de l'Eau et de l'Environnement de Strasbourg (ENGEES)-Université de Strasbourg (UNISTRA)-Institut National des Sciences Appliquées - Strasbourg (INSA Strasbourg), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Les Hôpitaux Universitaires de Strasbourg (HUS)-Centre National de la Recherche Scientifique (CNRS)-Matériaux et Nanosciences Grand-Est (MNGE), Université de Strasbourg (UNISTRA)-Université de Haute-Alsace (UHA) Mulhouse - Colmar (Université de Haute-Alsace (UHA))-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)
Subjects: Mathematical optimization, Control and Optimization, 49K15, 49J15, SIR epidemic model, Interval (mathematics), Management Science and Operations Research, 93C15, 01 natural sciences, Article, 010104 statistics & probability, 03 medical and health sciences, 92D30, herd immunity, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, Limit (mathematics), 0101 mathematics, SIMPLE algorithm, 030304 developmental biology, Mathematics, 0303 health sciences, Applied Mathematics, Optimal control, epidemic final size, 34H05, lockdown policy, Theory of computation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Minification, Epidemic model
Abstract: International audience; The aim of this article is to understand how to apply partial or total containment to SIR epidemic model during a given finite time interval in order to minimize the epidemic final size, that is the cumulative number of cases infected during the complete course of an epidemic. The existence and uniqueness of an optimal strategy is proved for this infinite-horizon problem and a full characterization of the solution is provided. The best policy consists in applying the maximal allowed social distancing effort until the end of the interval, starting at a date that is not always the closest date and may be found by a simple algorithm. Both theoretical results and numerical simulations demonstrate that it leads to a significant decrease of the epidemic final size. We show that in any case the optimal intervention has to begin before the number of susceptible cases has crossed the herd immunity level, and that its limit is always smaller than this threshold. This problem is also shown to be equivalent to the minimum containment time necessary to stop at a given distance after this threshold value.
Published: 2021

27. Comparison of models for the simulation of landslide generated Tsunamis

Author: Joao Guilherme Caldas Steinstraesser, Martin Parisot, Louis Emerald, Philippe Heinrich, Alexandre Paris, Emmanuel Audusse, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Littoral, Environnement : Méthodes et Outils Numériques (LEMON), 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), Institut de Recherche Mathématique de Rennes (IRMAR), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Laboratoire de Détection et de Géophysique (CEA) (LDG), DAM Île-de-France (DAM/DIF), Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction des Applications Militaires (DAM), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire des Sciences de l'Ingénieur Appliquées à la Mécanique et au génie Electrique (SIAME), Université de Pau et des Pays de l'Adour (UPPA), Certified Adaptive discRete moDels for robust simulAtions of CoMplex flOws with Moving fronts (CARDAMOM), Institut de Mathématiques de Bordeaux (IMB), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest
Subjects: [PHYS.PHYS.PHYS-FLU-DYN]Physics [physics]/Physics [physics]/Fluid Dynamics [physics.flu-dyn], [PHYS.PHYS.PHYS-AO-PH]Physics [physics]/Physics [physics]/Atmospheric and Oceanic Physics [physics.ao-ph], T57-57.97, Applied mathematics. Quantitative methods, 010504 meteorology & atmospheric sciences, Minimization problem, [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], Landslide, Mechanics, 01 natural sciences, Displacement (vector), 010305 fluids & plasmas, Physics::Geophysics, Waves and shallow water, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], 0103 physical sciences, QA1-939, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Limit (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Geology, Mathematics, 0105 earth and related environmental sciences
Abstract: International audience; In this paper, we analyze the relevance of the use of the shallow water model and the Boussinesq model to simulate tsunamis generated by a landslide. In a first part, we determine if the two models are able to reproduce waves generated by a landslide. Each model has drawbacks but it seems that it is possible to use them together to improve the simulations. In a second part we try to recover the landslide displacement from the generated wave. This problem is formulated as a minimization problem and we limit the number of parameters to determine assuming that the bottom can be well described by an empirical law.; Dans cet article, nous analysons la pertinence de l'utilisation de modèles intégrés suivant la verticale tels que le modèle de Saint-Venant et le modèle de Boussinesq pour simuler les tsunamis générés par un glissement de terrain. Dans une première partie, nous déterminons si les deux modèles sont capables de reproduire les vagues générées par un glissement de terrain. Chaque modèle présente des inconvénients mais il semble qu'il soit possible de les utiliser ensemble pour améliorer les simulations. Dans une deuxième partie, nous essayons de retrouver le déplacement du glissement de terrain à partir de la vague générée. Ce problème a été formulé comme un problème de minimisation et nous limitons le nombre de paramètres à déterminer en supposant que le fond peut être bien décrit par une loi empirique.
Published: 2021

28. Numerical Scheme for Kinetic Transport Equation with Internal State

Author: Nicolas Vauchelet, Shugo Yasuda, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, and University of Hyogo
Subjects: Discretization, Monte Carlo method, General Physics and Astronomy, 010103 numerical & computational mathematics, Asymptotic-preserving scheme, Kinetic energy, 01 natural sciences, Quantitative Biology::Cell Behavior, Mathematics - Analysis of PDEs, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Statistical physics, chemotaxis, 0101 mathematics, Scaling, Variable (mathematics), Physics, Mesoscopic physics, Ecological Modeling, kinetic-transport model with internal state, General Chemistry, State (functional analysis), Computer Science Applications, 010101 applied mathematics, Well-balanced scheme, Modeling and Simulation, Convection–diffusion equation, Analysis of PDEs (math.AP)
Abstract: International audience; We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level. It adds a variable in the mathematical model, which makes it more challenging to simulate numerically. Moreover, it has been shown that the macroscopic or mesoscopic quantities computed from this system converge to the Keller-Segel system at diffusive scaling or to the velocity-jump kinetic system for chemotaxis at hyperbolic scaling. Then we pay attention to propose numerical schemes uniformly accurate with respect to the scaling parameter. We show that these schemes converge to some limiting schemes which are consistent with the limiting macroscopic or kinetic system. This study is illustrated with some numerical simulations and comparisons with Monte Carlo simulations.
Published: 2021

29. A WELL-POSED AND EFFECTIVE HIGH-ORDER IMPEDANCE BOUNDARY CONDITION FOR THE TIME-HARMONIC SCATTERING PROBLEM FROM A MULTILAYER COATED 3-D OBJECT

Author: Stupfel, Bruno, Payen, Pierre, Lafitte, Olivier, Commissariat à l'Energie Atomique et aux Energies Alternatives (CEA-CESTA), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Centre de Recherches Mathématiques [Montréal] (CRM), and Université de Montréal (UdeM)
Subjects: [PHYS]Physics [physics], [MATH]Mathematics [math], Electrical and Electronic Engineering, Condensed Matter Physics, Electronic, Optical and Magnetic Materials
Abstract: International audience; The time-harmonic scattering problem from an isotropic multilayer coated 3-D object is considered. The coating is modeled by an impedance boundary condition (IBC) prescribed on the outer surface of the coating. The standard Leontovich IBC is local and constitutes a poor approximation for low index materials. A possible remedy is to employ high order IBCs (HOIBCs) involving tangential differential operators multiplied by coefficients. A generic HOIBC formulation (termed here IBC3) with five coefficients is considered here. Sufficient uniqueness conditions (SUCs) are derived for the corresponding Maxwell's problem (i.e., Maxwell's equations in free-space, radiation condition at infinity and IBC3 on the surface). The IBC3 coefficients are obtained by minimizing, with the SUCs as constraints, the error between either the exact and IBC3 impedances (local planar approximation) or the exact and IBC3 Mie series coefficients (local spherical approximation). Finally, the IBC3 is numerically implemented in a well-posed EFIE+MFIE formulation. Numerical results obtained on 3D objects demonstrate the high accuracy achieved with the constrained IBC3.
Published: 2021

30. The sterile insect technique used as a barrier control against reinfestation

Author: Almeida, Luis, Estrada, Jorge, Vauchelet, Nicolas, Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Modelling and Analysis for Medical and Biological Applications (MAMBA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Roland Herzog, Matthias Heinkenschloss, Dante Kalise, and Georg Stadler and Emmanuel Trélat
Subjects: Reaction-diffusion equations, Wave-blocking, fungi, Sterile insect technique, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Abstract: International audience; The sterile insect technique consists in massive release of sterilized males in the aim to reduce the size of mosquitoes population or even eradicate it. In this work, we investigate the feasability of using the sterile insect technique as a barrier against reinvasion. More precisely, we provide some numerical simulations and mathematical results showing that performing the sterile insect technique on a band large enough may stop reinvasion.
Published: 2022

31. Seriation in Combinatorial and Statistical Data Analysis

Author: Lerman, Israël César, Leredde, Henri, Institut de Recherche en Informatique et Systèmes Aléatoires (IRISA), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université de Bretagne Sud (UBS)-École normale supérieure - Rennes (ENS Rennes)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: [INFO]Computer Science [cs], [MATH]Mathematics [math]
Abstract: International audience
Published: 2022

32. Singular manifolds of proteomic drivers to model the evolution of inflammatory bowel disease status

Author: Assiya Marah, Thibaut Léger, Hatem Zaag, Eric Ogier-Denis, Isabelle Pic, Ian Morilla, Centre de recherche sur l'Inflammation (CRI (UMR_S_1149 / ERL_8252 / U1149)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Institut Jacques Monod (IJM (UMR_7592)), Université de Paris (UP)-Centre National de la Recherche Scientifique (CNRS), Institut de recherche en santé, environnement et travail (Irset), Université d'Angers (UA)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-École des Hautes Études en Santé Publique [EHESP] (EHESP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Structure Fédérative de Recherche en Biologie et Santé de Rennes ( Biosit : Biologie - Santé - Innovation Technologique ), 10-LABX-0017, Agence Nationale de la Recherche, Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Centre de recherche biomédicale Bichat-Beaujon (CRB3), Université Paris Diderot - Paris 7 (UPD7)-Institut National de la Santé et de la Recherche Médicale (INSERM), Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Université d'Angers (UA)-Université de Rennes (UR)-École des Hautes Études en Santé Publique [EHESP] (EHESP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Structure Fédérative de Recherche en Biologie et Santé de Rennes ( Biosit : Biologie - Santé - Innovation Technologique )
Subjects: Proteomics, 0301 basic medicine, Disease status, Proteome, Molecular biology, Computer science, [SDV]Life Sciences [q-bio], lcsh:Medicine, Disease, Inflammatory bowel disease, 0302 clinical medicine, Crohn Disease, lcsh:Science, 0303 health sciences, Gastrointestinal tract, Multidisciplinary, Molecular medicine, Drug discovery, Gastroenterology, Inflammatory Bowel Diseases, [SDV.BIBS]Life Sciences [q-bio]/Quantitative Methods [q-bio.QM], Manifold, Graph, Disease Progression, 030211 gastroenterology & hepatology, Disease Susceptibility, Inflammation Mediators, Systems biology, Algorithms, Immunology, Biophysics, Computational biology, Models, Biological, Article, 03 medical and health sciences, medicine, Humans, 030304 developmental biology, lcsh:R, Computational Biology, Reproducibility of Results, [MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT], medicine.disease, Chronic disorders, Computational biology and bioinformatics, 030104 developmental biology, Colitis, Ulcerative, lcsh:Q, Laplacian matrix, Biomarkers, 030217 neurology & neurosurgery
Abstract: The conditions used to describe the presence of an immune disease are often represented by interaction graphs. These informative, but intricate structures are susceptible to perturbations at different levels. The mode in which that perturbation occurs is still of utmost importance in areas such as cell reprogramming and therapeutics models. In this sense, module identification can be useful to well characterise the global graph architecture. To help us with this identification, we perform topological overlap-related measures. Thanks to these measures, the location of highly disease-specific module regulators is possible. Such regulators can perturb other nodes, potentially causing the entire system to change behaviour or collapse. We provide a geometric framework explaining such situations in the context of inflammatory bowel diseases (IBD). IBD are severe chronic disorders of the gastrointestinal tract whose incidence is dramatically increasing worldwide. Our approach models different IBD status as Riemannian manifolds defined by the graph Laplacian of two high throughput proteome screenings. It also identifies module regulators as singularities within the manifolds (the so-called singular manifolds). Furthermore, it reinterprets the characteristic nonlinear dynamics of IBD as compensatory responses to perturbations on those singularities. Then, particular reconfigurations of the immune system could make the disease status move towards an innocuous target state.
Published: 2020

33. On the power of template attacks in highly multivariate context

Author: Sylvain Guilley, Nadia El Mrabet, Philippe Guillot, Maamar Ouladj, Gilles Millérioux, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Laboratoire Traitement et Communication de l'Information (LTCI), Institut Mines-Télécom [Paris] (IMT)-Télécom Paris, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Polytechnique de Paris (IP Paris), Département Communications & Electronique (COMELEC), Télécom ParisTech, Secure and Safe Hardware (SSH), and Institut Mines-Télécom [Paris] (IMT)-Télécom Paris-Institut Mines-Télécom [Paris] (IMT)-Télécom Paris
Subjects: Computer Networks and Communications, Computer science, Computation, template attacks, Cryptography, 0102 computer and information sciences, 02 engineering and technology, computer.software_genre, 01 natural sciences, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], Software, 0202 electrical engineering, electronic engineering, information engineering, success rate, Implementation, dimensionality reduction, business.industry, Dimensionality reduction, Cryptographic protocol, Linear subspace, 020202 computer hardware & architecture, Information sensitivity, multivariate traces, Masking, 010201 computation theory & mathematics, signal-to-noise ratio, Data mining, business, spectral approach for computational speed improvement, computer
Abstract: International audience; When implemented in software (or hardware), a cryptographic protocol can leak sensitive information during its execution. Side-channel attacks can use those leakages in order to reveal some information about the secret used by the algorithm. The leaking side-channel information can take place in many time samples. Measurement appliances can cope with the acquisition of multiple samples. From an adversarial point of view, it is therefore beneficial to attempt to make the most of highly multivariate traces. On the one hand, template attacks have been introduced to deal with multivariate leakages, with as few assumptions as possible on the leakage model. On the other hand, many works have underlined the need for dimensionality reduction. In this paper, we clarify the relationship between template attacks in full space and in linear subspaces, in terms of success rate. In particular, we exhibit a clear mathematical expression for template attacks, which enables an efficient computation even on large dimensions such as several hundred of samples. It is noteworthy that both of PoI-based and PCA-based template attacks can straightforwardly benefit from our approach. Furthermore, we extend the approach to the masking-based protected implementations. Our approach is validated both by simulated and real-world traces.
Published: 2020

34. Chain-referral sampling on stochastic block models

Author: Thi Phuong Thuy Vo, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Statistics and Probability, Population, 0102 computer and information sciences, 01 natural sciences, Combinatorics, 010104 statistics & probability, Stochastic block model, FOS: Mathematics, Hidden populations, [MATH]Mathematics [math], 0101 mathematics, Chain-referral sampling, education, Mathematics, Random graph, education.field_of_study, Markov chain, Stochastic process, Probability (math.PR), Ode, exploration process, stochastic block model, Discrete time and continuous time, 010201 computation theory & mathematics, social network, respondent driven sampling, large graph limit, Mathematics - Probability, random graph
Abstract: The discovery of the “hidden population”, whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling (CRS) method, where participants recommend the people they know. This leads to the study of a Markov chain on a random graph where vertices represent individuals and edges connecting any two nodes describe the relationships between corresponding people. We are interested in the study of CRS process on the stochastic block model (SBM), which extends the well-known Erdös-Rényi graphs to populations partitioned into communities. The SBM considered here is characterized by a number of verticesN, a number of communities (blocks)m, proportion of each communityπ= (π1, …,πm) and a pattern for connection between blocksP= (λkl∕N)(k,l)∈{1,…,m}2. In this paper, we give a precise description of the dynamic of CRS process in discrete time on an SBM. The difficulty lies in handling the heterogeneity of the graph. We prove that when the population’s size is large, the normalized stochastic process of the referral chain behaves like a deterministic curve which is the unique solution of a system of ODEs.
Published: 2020

35. The extremal point process of branching Brownian motion in $\R^d$

Author: Berestycki, Julien, Kim, Yujin, Lubetzky, Eyal, Mallein, Bastien, Zeitouni, Ofer, Department of Statistics [Oxford], University of Oxford [Oxford], Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Department of Mathematics (Weizmann Institute of Science), and Weizmann Institute of Science [Rehovot, Israël]
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]
Abstract: We consider a branching Brownian motion in $\R^d$ with $d \geq 1$ in which the position $X_t^{(u)}\in \R^d$ of a particle $u$ at time $t$ can be encoded by its direction $\theta^{(u)}_t \in \S^{d-1}$ and its distance $R^{(u)}_t$ to 0. We prove that the \emph{extremal point process} $\sum \delta_{\theta^{(u)}_t, R^{(u)}_t - m_t^{(d)}}$ (where the sum is over all particles alive at time $t$ and $m^{(d)}_t$ is an explicit centring term) converges in distribution to a randomly shifted decorated Poisson point process on $\S^{d-1} \times \R$. More precisely, the so-called {\it clan-leaders} form a Cox process with intensity proportional to $D_\infty(\theta) e^{-\sqrt{2}r} \d r\d \theta $, where $D_\infty(\theta)$ is the limit of the derivative martingale in direction $\theta$ and the decorations are i.i.d.\ copies of the decoration process of the standard one-dimensional branching Brownian motion.This proves a conjecture of Stasi\'nski, Berestycki and Mallein (Ann.\ Inst.\ H.\ Poincar\'{e} 57:1786--1810, 2021), and builds on that paper andon Kim, Lubetzky and Zeitouni (arXiv:2104.07698).
Published: 2022

36. On the length of the shortest path in a sparse Barak-Erd\H{o}s graph

Author: Mallein, Bastien, Tesemnikov, Pavel, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Institute of Mathematics [Novosibirsk], and Institute of Mathematics of Novosibirsk
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 05C80, 05C20, 60F05, Mathematics - Probability
Abstract: We consider an inhomogeneous version of the Barak-Erd\H{o}s graph, i.e. a directed Er\H{o}s-R\'enyi random graph on $\{1,\ldots,n\}$ with no loop. Given $f$ a Riemann-integrable non-negative function on $[0,1]^2$ and $\gamma > 0$, we define $G(n,f,\gamma)$ as the random graph with vertex set $\{1,\ldots,n\}$ such that for each $i < j$ the directed edge $(i,j)$ is present with probability $ p_{i, j}^{(n)} = \frac{f(i/n,j/n)}{n^\gamma}$, independently of any other edge. We denote by $L_n$ the length of the shortest path between vertices $1$ and $n$, and take interest in the asymptotic behaviour of $L_n$ as $n \to \infty$.
Published: 2022

37. Energy stable and linearly well-balanced numerical schemes for the non-linear Shallow Water equations with Coriolis force

Author: Audusse, Emmanuel, Dubos, Virgile, Gaveau, Noémie, Penel, Yohan, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics (LHSV), École des Ponts ParisTech (ENPC)-Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement (Cerema)-EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Institut Denis Poisson (IDP), Université d'Orléans (UO)-Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire d'Hydraulique Saint-Venant / Saint-Venant laboratory for Hydraulics (Saint-Venant), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO)
Subjects: Physics::Atmospheric and Oceanic Physics, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: This work is dedicated to the analysis of a class of energy stable and linearly well-balanced numerical schemes dedicated to the non-linear Shallow Water equations with Coriolis force. The proposed algorithms rely on colocated finite volume approximations formulated on cartesian geometries. They involve appropriate diffusion terms in the numerical fluxes, expressed as discrete versions of the linear geostrophic equilibrium. We show that the resulting methods ensure semi-discrete energy estimates and numerical results show a very clear improvement around the nonlinear geostrophic equilibrium when compared to those of classic Godunov-type schemes.
Published: 2022

38. DicoPart - le dictionnaire critique et interdisciplinaire de la participation, la démocratie et la citoyenneté [2e édition]

Author: Guillaume Petit, Loïc Blondiaux, Ilaria Casillo, Jean-Michel Fourniau, Guillaume Gourgues, Samuel Hayat, Rémi Lefebvre, Sandrine Rui, Stéphanie Wojcik, Jodelle Zetlaoui-Leger, Petit, Guillaume, Guillaume Petit, Comité scientifique : Loïc Blondiaux, Ilaria Casillo, Jean-Michel Fourniau, Guillaume Gourgues, Samuel Hayat, Rémi Lefebvre, Guillaume Petit, Sandrine Rui, Stéphanie Wojcik, et Jodelle Zetlaouï-Léger, Assistance éditoriale : Julie Plouhinec, M2 en science politique, Maison des sciences de l'Homme Paris Nord (MSHPN), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, GIS Démocratie et Participation, Centre européen de sociologie et de science politique (CESSP), Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), Université Paris 1 Panthéon-Sorbonne (UP1), commission nationale du débat public (CNDP), Université Gustave Eiffel, Triangle : action, discours, pensée politique et économique (TRIANGLE), École normale supérieure de Lyon (ENS de Lyon)-Université Lumière - Lyon 2 (UL2)-Sciences Po Lyon - Institut d'études politiques de Lyon (IEP Lyon), Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de recherches politiques de Sciences Po (Sciences Po, CNRS) (CEVIPOF), Sciences Po (Sciences Po)-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes et de Recherches Administratives, Politiques et Sociales - UMR 8026 (CERAPS), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre Émile Durkheim (CED), Sciences Po Bordeaux - Institut d'études politiques de Bordeaux (IEP Bordeaux)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes des discours, Images, Textes, Ecrits, Communications (CEDITEC), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS), Comité scientifique : Loïc Blondiaux, Ilaria Casillo, Jean-Michel Fourniau, Guillaume Gourgues, Samuel Hayat, Rémi Lefebvre, Sandrine Rui, Stéphanie Wojcik, and et Jodelle Zetlaouï-Léger
Subjects: [SHS.ANTHRO-SE] Humanities and Social Sciences/Social Anthropology and ethnology, [SHS.SOCIO]Humanities and Social Sciences/Sociology, [SHS.DROIT] Humanities and Social Sciences/Law, [SHS.SOCIO] Humanities and Social Sciences/Sociology, [SHS.GEO] Humanities and Social Sciences/Geography, Citoyenneté, [SHS.PHIL]Humanities and Social Sciences/Philosophy, Participation, [SHS.GEO]Humanities and Social Sciences/Geography, [SHS.ANTHRO-SE]Humanities and Social Sciences/Social Anthropology and ethnology, [SHS.SCIPO]Humanities and Social Sciences/Political science, Démocratie, [SHS.PHIL] Humanities and Social Sciences/Philosophy, [SHS.DROIT]Humanities and Social Sciences/Law, Mouvement social, [SHS.SCIPO] Humanities and Social Sciences/Political science, Participation citoyenne
Abstract: Le Dictionnaire critique et interdisciplinaire de la Participation, DicoPart constitue une ressource pour les études sur la participation, la démocratie et la citoyenneté. Il vise à rendre compte, à partager et à structurer les enjeux, les débats et les apports des recherches dans ce domaine d’étude dans l’espace francophone, pour toutes les disciplines des sciences humaines et sociales. La participation est un thème structurant des sciences sociales, qui a profondément renouvelé des approches de théories politiques et des perspectives sociologiques. Cette publication centrale et accessible s’adresse aux étudiant·es, enseignant·es, chercheur·es, praticien·nes et citoyen·nes qui s’intéressent aux enjeux de démocratie et de participation, afin de les soutenir et les outiller dans leurs pratiques et leurs réflexions.https://www.dicopart.fr/
Published: 2022

39. Dictionnaire critique et interdisciplinaire de la Participation, 2ème édition: https://www.dicopart.fr

Author: Petit, Guillaume, Blondiaux, Loïc, Casillo, Ilaria, Fourniau, Jean-Michel, Gourgues, Guillaume, Hayat, Samuel, Lefebvre, Rémi, Rui, Sandrine, Wojcik, Stéphanie, Zetlaoui-Leger, Jodelle, Maison des sciences de l'Homme Paris Nord (MSHPN), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, GIS Démocratie et Participation, Centre européen de sociologie et de science politique (CESSP), Université Paris 1 Panthéon-Sorbonne (UP1)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), commission nationale du débat public (CNDP), Université Gustave Eiffel, Triangle : action, discours, pensée politique et économique (TRIANGLE), École normale supérieure - Lyon (ENS Lyon)-Université Lumière - Lyon 2 (UL2)-Sciences Po Lyon - Institut d'études politiques de Lyon (IEP Lyon), Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de recherches politiques de Sciences Po (Sciences Po, CNRS) (CEVIPOF), Sciences Po (Sciences Po)-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes et de Recherches Administratives, Politiques et Sociales - UMR 8026 (CERAPS), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centre Émile Durkheim (CED), Sciences Po Bordeaux - Institut d'études politiques de Bordeaux (IEP Bordeaux)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Centre d'Etudes des discours, Images, Textes, Ecrits, Communications (CEDITEC), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12), École nationale supérieure d'architecture de Paris Val-de-Seine (ENSA PVDS), Guillaume Petit, Comité scientifique : Loïc Blondiaux, Ilaria Casillo, Jean-Michel Fourniau, Guillaume Gourgues, Samuel Hayat, Rémi Lefebvre, Sandrine Rui, Stéphanie Wojcik, et Jodelle Zetlaouï-Léger, and Assistance éditoriale : Julie Plouhinec, M2 en science politique
Subjects: Démocratie, [SHS.DROIT]Humanities and Social Sciences/Law, [SHS.SOCIO]Humanities and Social Sciences/Sociology, Citoyenneté, Participation, [SHS.PHIL]Humanities and Social Sciences/Philosophy, [SHS.GEO]Humanities and Social Sciences/Geography, [SHS.ANTHRO-SE]Humanities and Social Sciences/Social Anthropology and ethnology, Mouvement social, Participation citoyenne, [SHS.SCIPO]Humanities and Social Sciences/Political science
Abstract: Le Dictionnaire critique et interdisciplinaire de la Participation, DicoPart constitue une ressource pour les études sur la participation, la démocratie et la citoyenneté. Il vise à rendre compte, à partager et à structurer les enjeux, les débats et les apports des recherches dans ce domaine d’étude dans l’espace francophone, pour toutes les disciplines des sciences humaines et sociales. La participation est un thème structurant des sciences sociales, qui a profondément renouvelé des approches de théories politiques et des perspectives sociologiques. Cette publication centrale et accessible s’adresse aux étudiant·es, enseignant·es, chercheur·es, praticien·nes et citoyen·nes qui s’intéressent aux enjeux de démocratie et de participation, afin de les soutenir et les outiller dans leurs pratiques et leurs réflexions.
Published: 2022

40. Scattering rigidity for analytic metrics

Author: Yannick Guedes Bonthonneau, Colin Guillarmou, Malo Jézéquel, Université Sorbonne Paris Nord, Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Paris-Saclay, Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, United States, European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 787304), European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 725967), PRC grant ADYCT (ANR-20-CE40-0017), ANR-20-CE40-0017,ADYCT,Aléatoire, dynamique et spectre(2020), European Project: 725967,IPFLOW, European Project: 787304,SOS, Jézéquel, Malo, Aléatoire, dynamique et spectre - - ADYCT2020 - ANR-20-CE40-0017 - AAPG2020 - VALID, Inverse Problems and Flows - IPFLOW - 725967 - INCOMING, and Smooth dynamics via Operators, with Singularities - SOS - 787304 - INCOMING
Subjects: Mathematics - Differential Geometry, Mathematics - Analysis of PDEs, Differential Geometry (math.DG), 37D20, 37D40, 35R30, FOS: Mathematics, [MATH] Mathematics [math], Mathematics::Differential Geometry, Dynamical Systems (math.DS), [MATH]Mathematics [math], Mathematics - Dynamical Systems, Analysis of PDEs (math.AP)
Abstract: For analytic negatively curved Riemannian manifold with analytic strictly convex boundary, we show that the scattering map for the geodesic flow determines the manifold up to isometry. In particular one recovers both the topology and the metric. More generally, our result holds in the analytic category under the no conjugate point and hyperbolic trapped sets assumptions., Comment: v2: added Propositions 2.6 and 2.7 and Appendix B
Published: 2022
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41. Scattering for critical radial Neumann waves outside a ball

Author: Thomas Duyckaerts, David Lafontaine, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Institut de Mathématiques de Toulouse UMR5219 (IMT), 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: Scattering, General Mathematics, Mathematical analysis, Mathematics::Analysis of PDEs, Rigidity (psychology), Wave equation, Mathematics - Analysis of PDEs, Scheme (mathematics), Neumann boundary condition, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Data scatter, 35L70 (Primary) 34B15, 34D05 (Secondary), Ball (mathematics), Energy (signal processing), Mathematics, Analysis of PDEs (math.AP)
Abstract: We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a nonlinear wave equation with Neumann boundary conditions. Our proof uses the scheme of concentration-compactness/rigidity introduced by Kenig and Merle, extending it to our setup, together with the so-called channels of energy method to rule out compact-flow solutions. We also obtain, for the focusing equation, the same exact scattering/blow-up dichotomy below the energy of the ground-state as in $\mathbb R^3$.
Published: 2022

42. Numerical resolution of the inverse source problem for EEG using the quasi-reversibility method

Author: Darbas, Marion, Leblond, Juliette, Marmorat, Jean-Paul, Tournier, Pierre-Henri, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Analyse fonctionnelle pour la conception et l'analyse de systèmes (FACTAS), 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), Centre de Mathématiques Appliquées (CMA), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Algorithms and parallel tools for integrated numerical simulations (ALPINES), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)
Subjects: Inverse problems, best constrained approximation, brain imaging (EEG), elliptic PDE, quasi-reversibility, [MATH]Mathematics [math], Inverse problems elliptic PDE quasi-reversibility best constrained approximation brain imaging (EEG)
Abstract: Soumis pour publication.; International audience; We propose a numerical method for solving a family of source estimation inverse problems from Cauchy data for Poisson (conductivity) PDE in non-homogeneous domains. The targeted application is the electroencephalography (EEG) dipolar source localization problem in brain imaging, for which it allows to take into account the specific heterogeneity of the skull in the data transmission step (cortical mapping) from the scalp to the cortex.
Published: 2022

43. Orbital stability of ground states for a Sobolev critical Schrödinger equation

Author: Louis Jeanjean, Jacek Jendrej, Thanh Trung Le, Nicola Visciglia, Jacek, Jendrej, APPEL À PROJETS GÉNÉRIQUE 2018 - Etudes de solutions spéciales pour des équations dispersives - - ESSED2018 - ANR-18-CE40-0028 - AAPG2018 - VALID, Laboratoire de Mathématiques de Besançon (UMR 6623) (LMB), Université de Bourgogne (UB)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Dipartimento di Matematica [Pisa], University of Pisa - Università di Pisa, and ANR-18-CE40-0028,ESSED,Etudes de solutions spéciales pour des équations dispersives(2018)
Subjects: Mathematics - Analysis of PDEs, Applied Mathematics, General Mathematics, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Analysis of PDEs (math.AP)
Abstract: We study the existence of ground state standing waves, of prescribed mass, for the nonlinear Schr\"{o}dinger equation with mixed power nonlinearities \begin{equation*} i \partial_t v + \Delta v + \mu v |v|^{q-2} + v |v|^{2^* - 2} = 0, \quad (t, x) \in \mathbb{R} \times \mathbb{R}^N, \end{equation*} where $N \geq 3$, $v: \mathbb{R} \times \mathbb{R}^N \to \mathbb{C}$, $\mu > 0$, $2 < q < 2 + 4/N $ and $2^* = 2N/(N-2)$ is the critical Sobolev exponent. We show that all ground states correspond to local minima of the associated Energy functional. Next, despite the fact that the nonlinearity is Sobolev critical, we show that the set of ground states is orbitally stable. Our results settle a question raised by N. Soave [35]., Comment: This version is the final one, corresponding to the paper now published in Journal de Math\'ematiques Pures et Appliqu\'ees : https://doi.org/10.1016/j.matpur.2022.06.005
Published: 2022

44. A Component-Based Data Assimilation Strategy with Applications to Vascular Flows

Author: Bui, Duc-Quang, Mollo, Pierre, Nobile, Fabio, Taddei, Tommaso, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Laboratoire de Mathématiques de Reims (LMR), Université de Reims Champagne-Ardenne (URCA)-Centre National de la Recherche Scientifique (CNRS), Ecole Polytechnique Fédérale de Lausanne (EPFL), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), 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)-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)-Inria Bordeaux - Sud-Ouest, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We present a parameterized-background data-weak (PBDW) approach [Y Maday, AT Patera, JD Penn, M Yano, Int J Numer Meth Eng, 102(5), 933-965] to the steady-state variational data assimilation (DA) problem for systems modeled by partial differential equations (PDEs) and characterized by multiple interconnected components, with emphasis on vascular flows. We focus on the problem of reconstructing the state of the system in one specific component, based on local measurements. The PBDW approach does not require the solution of any PDE model at prediction stage (projection-by-data) and, as such, enables local state estimates on single components, as long as good background and update spaces for the estimation can be constructed. We discuss the application of PBDW to a two-dimensional steady Navier-Stokes problem for a family of parameterized geometries, and investigate instead the effects of enforcing no-slip boundary conditions and incompressibility constraints on the background and update spaces to enhance the state estimation. Furthermore, we show an actionable strategy to train local reduced-order bases (ROBs) for the background space that can later be used for DA tasks.
Published: 2022

45. Enriched nonconforming multiscale finite element method for Stokes flows in heterogeneous media based on high-order weighting functions

Author: Qingqing Feng, Gregoire Allaire, Pascal Omnes, CEA- Saclay (CEA), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Mécanique des Fluides, Energies et Environnement (EDF R&D MFEE), EDF R&D (EDF R&D), EDF (EDF)-EDF (EDF), Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, and CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN))
Subjects: Multiscale Finite Element Method, Stokes Flows, 65N30, Crouzeix-Raviart Element, Ecological Modeling, Modeling and Simulation, General Physics and Astronomy, General Chemistry, 76M30, 76D07, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Computer Science Applications, Mathematics::Numerical Analysis
Abstract: International audience; This paper addresses an enriched nonconforming Multiscale Finite Element Method (MsFEM) to solve viscous incompressible flow problems in genuine heterogeneous or porous media. In the work of [B. P. Muljadi, J. Narski, A. Lozinski, and P. Degond, Multiscale Modeling \& Simulation 2015 13:4, 1146-1172] and [G. Jankowiak and A. Lozinski, arXiv:1802.04389 [math.NA], 2018], a nonconforming MsFEM has been first developed for Stokes problems in such media. Based on these works, we propose an innovative enriched nonconforming MsFEM where the approximation space of both velocity and pressure are enriched by weighting functions which are defined by polynomials of higher-degree. Numerical experiments show that this enriched nonconforming MsFEM improves significantly the accuracy of the nonconforming MsFEMs. Theoretically, this method provides a general framework which allows to find a good compromise between the accuracy of the method and the computing costs, by varying the degrees of polynomials.
Published: 2022

46. STABILITY AND LARGE-TIME BEHAVIOR FOR THE 2D BOUSSINEQ SYSTEM WITH VERTICAL DISSIPATION AND HORIZONTAL THERMAL DIFFUSION

Author: Ben Said, Oussama, Ben Said, Mona, Oklahoma State University [Stillwater], Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Mathematics - Analysis of PDEs, Hydrostatic balance, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Partial dissipation, Boussinesq equations, Stability, Decay rates, Analysis of PDEs (math.AP)
Abstract: The hydrostatic balance or hydrostatic equilibrium is one of the most prominent topics in fluid dynamics, atmospherics and astrophysics. In fact, our atmosphere is mainly in hydrostatic equilibrium, between the upward-directed pressure gradient force and the downward-directed force of gravity. Understanding the stability of perturbations near the hydrostatic balance of the Boussinesq system may help gain insight into some weather phenomena. This paper is concerned with the 2D anisotropic Boussinesq equations involving only vertical dissipation and horizontal thermal diffusion. When the spatial domain is $\Omega=\mathbb{T}\times\mathbb{R}$ with $\mathbb{T}= [0, 1]$ being a 1D periodic box, this work establishes the stability and specifies the precise large-time behavior of perturbations near the hydrostatic equilibrium. The approach here is to distinguish the vertical averages of the velocity and temperature from their corresponding oscillation parts., Comment: arXiv admin note: text overlap with arXiv:2009.13445 by other authors
Published: 2021

47. Valeurs extrêmes de processus de branchement spatiaux

Author: Belloum, Mohamed Ali, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord, Université Sorbonne Naris Nord, and Bastien Mallein
Subjects: processus extremal, extremal processes, processus de branchement multitypes, branching Brownian motion, Mouvement brownien branchant, Branching random walk, Marche aléatoire branchante, [MATH]Mathematics [math], multitype branching process, extremes of log-correlated random fields, valeurs extrêmes de champs aléatoires log-corréles
Abstract: In this thesis, we are interested in extreme values of certain spatial branching processes such as the branching random walk and the branching Brownian motion. The branching random walk is a particle system that can be described as follows. It starts with an unique particle at generation $0$. It gives birth to a random number of children positioned with respect to their parent according to a point process. Then, each child repeats the same process to that of his parent and independently of the rest of particles. The branching Brownian motion can be described similarly. It starts with an unique particle at the origin. It moves according to a standard Brownian motion. After an exponential time, it dies giving birth to two children on its current position. Then, each child starts an independent branching Brownian motion.In the first part of this thesis, we study a model that interpolates between the branching random walk and a model linked to statistical physics which called \textit{Random energy model (REM)}. The next part of this thesis is devoted to the study of the extreme values of certain multitype branching processes. More precisely, we study the asymptotic behaviour of the extremal process of a reducible branching Brownian motion.; Dans cette thèse, on s'intéresse aux valeurs extrêmes de certains processus de branchement spatiaux tels que la marche aléatoire branchante et le mouvement Brownien branchant. La marche aléatoire branchante est un système de particule qui peut être modélisé de la façon suivante. On part d'une seule particule à la génération $0$. Elle donne naissance à un nombre aléatoire d'enfants positionnés autour de leur parent selon un processus de points. Puis chaque enfant répète le même processus que celui de son parent indépendamment des autres particules. Le mouvement brownien branchant peut être décrit de manière similaire. On commence toujours avec une seule particule située à l'origine à l'instant $t=0$. Elle se déplace selon un mouvement Brownien standard. Après un temps exponentiel de paramètre $1$, elle meurt en donnant naissance à deux enfants. Puis chacun des deux enfants commence à son tour un mouvement Brownien branchant indépendant. Dans la première partie de cette thèse on étudie un modèle qui interpole entre la marche aléatoire branchante et un modèle lié à la physique statistique appelé \textit{Random Energy Model (REM)}. Le deuxième et le troisième chapitre sont consacrés à l'étude des valeurs extrêmes de certains modèles de branchement multitype. Plus précisément, on étudie le comportement asymptotique du processus extrémal d'un mouvement Brownien branchant multitype réductible.
Published: 2021

48. A Fourier Transform for Banach-Colmez spaces

Author: Anschütz, Johannes, Bras, Arthur-César Le, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Mathematics - Algebraic Geometry, Mathematics - Number Theory, Mathematics::Number Theory, [MATH]Mathematics [math], Mathematics::Representation Theory
Abstract: We define and study an $\ell$-adic Fourier transform for a relative version of Banach-Colmez spaces (over a perfectoid space which is not necessarily a geometric point), which can be thought of as some analytic analogue of the $\ell$-adic Fourier transform for unipotent perfect group schemes. We explicitly describe it on some examples.
Published: 2021

49. Averaging functors in Fargues' program for GL_n

Author: Anschütz, Johannes, Bras, Arthur-César Le, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Mathematics - Number Theory, 11S37, 22E57, Mathematics::Number Theory, [MATH]Mathematics [math], Mathematics::Representation Theory, Mathematics - Representation Theory
Abstract: We study the so-called averaging functors from the geometric Langlands program in the setting of Fargues' program. This makes explicit certain cases of the spectral action which was recently introduced by Fargues-Scholze in the local Langlands program for $\mathrm{GL}_n$. Using these averaging functors, we verify (without using local Langlands) that the Fargues-Scholze parameters associated to supercuspidal modular representations of $\mathrm{GL}_2$ are irreducible. We also attach to any irreducible $\ell$-adic Weil representation of degree $n$ an Hecke eigensheaf on $\mathrm{Bun}_n$, and show, using the local Langlands correspondence and recent results of Hansen and Kaletha-Weinstein, that it satisfies most of the requirements of Fargues' conjecture for $\mathrm{GL}_n$.
Published: 2021

50. The de Rham-Fargues-Fontaine cohomology

Author: Bras, Arthur-César Le, Vezzani, Alberto, Laboratoire Analyse, Géométrie et Applications (LAGA), and Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Université Sorbonne Paris Nord
Subjects: Mathematics - Algebraic Geometry, Mathematics - Number Theory, Mathematics::K-Theory and Homology, Mathematics - K-Theory and Homology, [MATH]Mathematics [math]
Abstract: We show how to attach to any rigid analytic variety $V$ over a perfectoid space $P$ a rigid analytic motive over the Fargues-Fontaine curve $\mathcal{X}(P)$ functorially in $V$ and $P$. We combine this construction with the overconvergent relative de Rham cohomology to produce a complex of solid quasi-coherent sheaves over $\mathcal{X}(P)$, and we show that its cohomology groups are vector bundles if $V$ is smooth and proper over $P$ or if $V$ is quasi-compact and $P$ is a perfectoid field, thus proving and generalizing a conjecture of Scholze. The main ingredients of the proofs are explicit $\mathbb{B}^1$-homotopies, the motivic proper base change and the formalism of solid quasi-coherent sheaves., Comment: 43 pages
Published: 2021

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