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1. Corrected Curvature Measures

Author: Jacques-Olivier Lachaud, Pascal Romon, Boris Thibert, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), ANR-15-CE40-0006,CoMeDiC,Métriques convergentes pour le calcul digital(2015), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Laboratoire d'Analyse et de Mathématiques Appliquées (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Fédération de Recherche Bézout-Université Paris-Est Marne-la-Vallée (UPEM), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Université Paris-Est Marne-la-Vallée (UPEM)-Fédération de Recherche Bézout-Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS), Calcul des Variations, Géométrie, Image (CVGI), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)
Subjects: Computational Theory and Mathematics, [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], Curvature estimators, Digital geometry, Discrete geometry, Discrete Mathematics and Combinatorics, Geometric measure theory, Geometry and Topology, MSC 52B70, 65D18, 49Q15, Normal cycle, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG], Theoretical Computer Science
Abstract: International audience; This paper proposes a new mathematical and computational tool for infering the geometry of shapes known only through approximations such as triangulated or digital surfaces. The main idea is to decouple the position of the shape boundary from its normal vector field. To do so, we extend a classical tool of geometric measure theory, the normal cycle, so that it takes as input not only a surface but also a normal vector field. We formalize it as a current in the oriented Grassmann bundle R^3 × S^2. By choosing adequate differential forms, we define geometric measures like area, mean and Gaussian curvatures. We then show the stability of these measures when both position and normal input data are approximations of the underlying continuous shape. As a byproduct, our tool is able to correctly estimate curvatures over polyhedral approximations of shapes with explicit bounds, even when their natural normal are not correct, as long as an external convergent normal vector field is provided. Finally, the accuracy, convergence and stability under noise perturbation is evaluated experimentally onto digital surfaces.
Published: 2022
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2. Homogenization of the eigenvalues of the Neumann-Poincaré operator

Author: Faouzi Triki, Eric Bonnetier, Charles Dapogny, Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles (EDP), AGIR-HOMONIM grant from Université Grenoble-Alpes and Labex PERSYVAL-Lab (ANR-11-LABX-0025-01)., ANR-11-LABX-0025-01,PERSYVAL-lab,Systèmes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Equations aux Dérivées Partielles (EDP ), and ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)
Subjects: Physics, Mechanical Engineering, 010102 general mathematics, Mathematical analysis, homogenization, Eigenfunction, 01 natural sciences, Neumann–Poincaré operator, Homogenization (chemistry), Potential theory, 010101 applied mathematics, symbols.namesake, Mathematics (miscellaneous), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Bounded function, Poincaré conjecture, symbols, plasmonic resonances, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Bloch waves, Analysis, Eigenvalues and eigenvectors, Bloch wave
Abstract: In this article, we investigate the spectrum of the Neumann–Poincare operator $${{\mathcal {K}}}_\varepsilon ^*$$ (or equivalently, that of the associated Poincare variational operator $$T_\varepsilon $$ ) associated to a periodic distribution of small inclusions with size $$\varepsilon $$ , and its asymptotic behavior as the parameter $$\varepsilon $$ vanishes. Combining techniques pertaining to the fields of homogenization and potential theory, we prove that the limit spectrum is composed of the ‘trivial’ eigenvalues 0 and 1, and of a subset which stays bounded away from 0 and 1 uniformly with respect to $$\varepsilon $$ . This non trivial part is the reunion of the Bloch spectrum, accounting for the collective resonances between collections of inclusions, and of the boundary layer spectrum, associated to eigenfunctions which spend a not too small part of their energies near the boundary of the macroscopic device. These results shed new light on the issue of the homogenization of the voltage potential $$u_\varepsilon $$ caused by a given source in a medium composed of a periodic distribution of small inclusions with an arbitrary (possible negative) conductivity a, surrounded by a dielectric medium, with unit conductivity. In particular, we prove that the limit behavior of $$u_\varepsilon $$ is strongly related to the (possibly ill-defined) homogenized diffusion matrix predicted by the homogenization theory in the standard elliptic case. Additionally, we prove that the homogenization of $$u_\varepsilon $$ is always possible when a is either positive, or negative with a ‘small’ or ‘large’ modulus.
Published: 2019
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3. Critical length: an alternative approach

Author: Marie-Laurence Mazure, Carolina Vittoria Beccari, Giulio Casciola, Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Beccari, Carolina Vittoria, Casciola, Giulio, and Mazure, Marie-Laurence
Subjects: Generalised derivative, Critical length (for design), Shape effect, Bernstein-type base, Applied Mathematics, Numerical analysis, Numerical Analysis (math.NA), 010103 numerical & computational mathematics, Differential operator, 01 natural sciences, Chebyshev filter, Critical length, 010101 applied mathematics, Extended Chebyshev space, Computational Mathematics, Bounded function, FOS: Mathematics, Applied mathematics, Mathematics - Numerical Analysis, [MATH]Mathematics [math], 0101 mathematics, Constant (mathematics), ComputingMilieux_MISCELLANEOUS, Shape preservation, Mathematics
Abstract: International audience; We provide a numerical method to determine the critical lengths of linear differential operators with constant real coefficients. The need for such a procedure arises when the orders increase. The interest of this article is clearly on the practical side since knowing the critical lengths permits an optimal use of the associated kernels. The efficiency of the procedure is due to its being based on crucial features of Extended Chebyshev spaces on closed bounded intervals.
Published: 2019
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4. Existence and regularity of optimal shapes for elliptic operators with drift

Author: Emmanuel Russ, Bozhidar Velichkov, Baptiste Trey, Russ, E., Trey, B., Velichkov, B., Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), and ANR-11-LABX-0025-01,PERSYVAL-lab,Systèmes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011)
Subjects: Open set, 01 natural sciences, Omega, Combinatorics, symbols.namesake, Mathematics - Analysis of PDEs, principal eigenvalue, Free boundary problem, FOS: Mathematics, laplacian with drift, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Nabla symbol, 0101 mathematics, Mathematics - Optimization and Control, Mathematics, Applied Mathematics, 010102 general mathematics, optimal shape, Lipschitz continuity, quasi-open set, free boundary problem, 010101 applied mathematics, Elliptic operator, Optimization and Control (math.OC), Bounded function, Dirichlet boundary condition, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis, Analysis of PDEs (math.AP)
Abstract: This paper is devoted to the study of shape optimization problems for the first eigenvalue of the elliptic operator with drift L = --$\Delta$+V (x)\cdot \nabla with Dirichlet boundary conditions, where V is a bounded vector field. In the first instance, we prove the existence of a principal eigenvalue $\lambda$\_1($\Omega$, V) for a bounded quasi-open set $\Omega$ which enjoys similar properties to the case of open sets. Then, given m > 0 and $\tau$ $\ge$ 0, we show that the minimum of the following non-variational problem min $\lambda$\_1($\Omega$, V) : $\Omega$ $\subset$ D quasi-open, |$\Omega$| $\le$ m, |V|\_{\infty} $\le$ $\tau$. is achieved, where the box D $\subset$ R^d is a bounded open set. The existence when V is fixed, as well as when V varies among all the vector fields which are the gradient of a Lipschitz function, are also proved. The second interest and main result of this paper is the regularity of the optimal shape $\Omega$ * solving the minimization problem min $\lambda$\_1($\Omega$, $\Phi$) : $\Omega$ $\subset$ D quasi-open, |$\Omega$| $\le$ m , where $\Phi$ is a given Lipschitz function on D. We prove that the topological boundary $\partial$$\Omega$ * is composed of a regular part which is locally the graph of a C ^{1,$\alpha$} function and a singular part which is empty if d < d * , discrete if d = d * and of locally finite H^{d--d *} Hausdorff measure if d > d * , where d * $\in$ {5, 6, 7} is the smallest dimension at which there exists a global solution to the one-phase free boundary problem with singularities. Moreover, if D is smooth, we prove that, for each x $\in$ $\partial$$\Omega$ * $\cap$ $\partial$D, $\partial$$\Omega$ * is C^{ 1,$\alpha$} in a neighborhood of x, for some $\alpha$ $\le$ 1 /2. This last result is optimal in the sense that C ^{1,1/2} is the best regularity that one can expect.
Published: 2019

5. Free boundary regularity for a multiphase shape optimization problem

Author: Baptiste Trey, Luca Spolaor, Bozhidar Velichkov, Massachusetts Institute of Technology (MIT), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), and VELICHKOV, Bozhidar
Subjects: the two-phase problem, Regularity of free boundaries, Boundary (topology), [MATH] Mathematics [math], 01 natural sciences, Alt-Caffarelli-Friedman, Alt-Caffarelli, Dirichlet eigenvalue, Mathematics - Analysis of PDEs, Dimension (vector space), FOS: Mathematics, almost-minimizers, Dirichlet eigenvalues, epiperimetric inequality, multiphase problems, shape optimization, the one-phase problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Shape optimization, Shape optimization problem, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH]Mathematics [math], Mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, 010101 applied mathematics, Analysis, Analysis of PDEs (math.AP)
Abstract: In this paper we prove a $C^{1,\alpha}$ regularity result in dimension two for almost-minimizers of the constrained one-phase Alt-Caffarelli and the two-phase Alt-Caffarelli-Friedman functionals for an energy with variable coefficients. As a consequence, we deduce the complete regularity of solutions of a multiphase shape optimization problem for the first eigenvalue of the Dirichlet-Laplacian up to the fixed boundary. One of the main ingredient is a new application of the epiperimetric-inequality of Spolaor-Velichkov [CPAM, 2018] up to the boundary. While the framework that leads to this application is valid in every dimension, the epiperimetric inequality is known only in dimension two, thus the restriction on the dimension.
Published: 2018

6. The plasmonic resonances of a bowtie antenna

Author: Faouzi Triki, Charles Dapogny, Eric Bonnetier, Hai Zhang, Institut Fourier (IF ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Equations aux Dérivées Partielles (EDP ), Hong Kong University of Science and Technology (HKUST), Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), and Equations aux Dérivées Partielles (EDP)
Subjects: business.industry, Applied Mathematics, 01 natural sciences, 010305 fluids & plasmas, 010101 applied mathematics, Mathematics - Analysis of PDEs, Optics, 0103 physical sciences, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Antenna (radio), business, Analysis, Plasmon, Mathematics, Analysis of PDEs (math.AP)
Abstract: International audience; Metallic bowtie-shaped nanostructures are very interesting objects in optics, due to their capability of localizing and enhancing electromagnetic fields in the vicinity of their central neck. In this article, we investigate the electrostatic plasmonic resonances of two-dimensional bowtie-shaped domains by looking at the spectrum of their Poincar\'e variational operator. In particular, we show that the latter only consists of essential spectrum and fills the whole interval $[0,1]$. This behavior is very different from what occurs in the counterpart situation of a bowtie domain with only close-to-touching wings, a case where the essential spectrum of the Poincar\'e variational operator is reduced to an interval strictly contained in $[0,1]$. We provide an explanation for this difference by showing that the spectrum of the Poincaré variational operator of bowtie-shaped domains with close-to-touching wings has eigenvalues which densify and eventually fill the remaining intervals as the distance between the two wings tends to zero.
Published: 2018
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7. Regularity of Minimizers of Shape Optimization Problems involving Perimeter

Author: Jimmy Lamboley, Guido De Philippis, Michel Pierre, Bozhidar Velichkov, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), École normale supérieure - Rennes (ENS Rennes), 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), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-12-BS01-0007 OPTIFORM, Agence Nationale de la Recherche, RBSI14RVEZ, MIUR, ANR-12-BS01-0007,OPTIFORM,Optimisation de Formes(2012), Unité de Mathématiques Pures et Appliquées ( UMPA-ENSL ), École normale supérieure - Lyon ( ENS Lyon ) -Centre National de la Recherche Scientifique ( CNRS ), CEntre de REcherches en MAthématiques de la DEcision ( CEREMADE ), Université Paris-Dauphine-Centre National de la Recherche Scientifique ( CNRS ), École normale supérieure - Rennes ( ENS Rennes ), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Calcul des Variations, Géométrie, Image ( CVGI ), Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), ANR-12-BS01-0007,OPTIFORM,Optimisation de Formes ( 2012 ), École normale supérieure de Lyon (ENS de Lyon)-Centre National de la Recherche Scientifique (CNRS), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), ANR-11-LABX-0020,LEBESGUE,Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation(2011), De Philippis, G., Lamboley, J., Pierre, M., and Velichkov, B.
Subjects: [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC], Spectral theory, regularity, General Mathematics, Spectral functional, Space (mathematics), 01 natural sciences, Omega, free boundary, Combinatorics, Shape optimization, Settore MAT/05 - Analisi Matematica, FOS: Mathematics, Mathematics (all), 0101 mathematics, Mathematics - Optimization and Control, Dirichlet energy, Regularity, Applied Mathematics, Mathematics, 010102 general mathematics, Dirichlet's energy, Function (mathematics), spectral theory, Lipschitz continuity, 010101 applied mathematics, Optimization and Control (math.OC), Bounded function, Domain (ring theory), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: We prove existence and regularity of optimal shapes for the problem$$\min\Big\{P(\Omega)+\mathcal{G}(\Omega):\ \Omega\subset D,\ |\Omega|=m\Big\},$$where $P$ denotes the perimeter, $|\cdot|$ is the volume, and the functional $\mathcal{G}$ is either one of the following:\textless{}ul\textgreater{}\textless{}li\textgreater{} the Dirichlet energy $E\_f$, with respect to a (possibly sign-changing) function $f\in L^p$;\textless{}/li\textgreater{}\textless{}li\textgreater{}a spectral functional of the form $F(\lambda\_{1},\dots,\lambda\_{k})$, where $\lambda\_k$ is the $k$th eigenvalue of the Dirichlet Laplacian and $F:\mathbb{R}^k\to\mathbb{R}$ is Lipschitz continuous and increasing in each variable.\textless{}/li\textgreater{}\textless{}/ul\textgreater{}The domain $D$ is the whole space $\mathbb{R}^d$ or a bounded domain. We also give general assumptions on the functional $\mathcal{G}$ so that the result remains valid., Comment: Journal de Math\'ematiques Pures et Appliqu\'ees, Elsevier, 2016
Published: 2018
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8. An algorithm for optimal transport between a simplex soup and a point cloud

Author: Quentin Mérigot, Jocelyn Meyron, Boris Thibert, Laboratoire de Mathématiques d'Orsay ( LMO ), Université Paris-Saclay-Centre National de la Recherche Scientifique ( CNRS ), AGPIG ( GIPSA-AGPIG ), Département Images et Signal ( GIPSA-DIS ), Grenoble Images Parole Signal Automatique ( GIPSA-lab ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Grenoble Images Parole Signal Automatique ( GIPSA-lab ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Calcul des Variations, Géométrie, Image ( CVGI ), Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), ANR-16-CE40-0014,MAGA,Monge-Ampère et Géométrie Algorithmique ( 2016 ), ANR-11-LABX-0025-01,PERSYVAL-lab,Systèmes et Algorithmes Pervasifs au confluent des mondes physique et numérique ( 2011 ), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), GIPSA - Architecture, Géométrie, Perception, Images, Gestes (GIPSA-AGPIG), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-16-CE40-0014,MAGA,Monge-Ampère et Géométrie Algorithmique(2016), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), and Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11)
Subjects: Computational Geometry (cs.CG), FOS: Computer and information sciences, Computer science, General Mathematics, Point cloud, 02 engineering and technology, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Measure (mathematics), 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Optimal transport, Power diagram, Mathematics - Numerical Analysis, 0101 mathematics, Simplex, Applied Mathematics, Numerical analysis, 020207 software engineering, Geometry processing, Numerical Analysis (math.NA), [ MATH.MATH-NA ] Mathematics [math]/Numerical Analysis [math.NA], 010101 applied mathematics, [ INFO.INFO-CG ] Computer Science [cs]/Computational Geometry [cs.CG], Computer Science - Computational Geometry, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We propose a numerical method to find the optimal transport map between a measure supported on a lower-dimensional subset of R^d and a finitely supported measure. More precisely, the source measure is assumed to be supported on a simplex soup, i.e. on a union of simplices of arbitrary dimension between 2 and d. As in [Aurenhammer, Hoffman, Aronov, Algorithmica 20 (1), 1998, 61–76] we recast this optimal transport problem as the resolution of a non-linear system where one wants to prescribe the quantity of mass in each cell of the so-called Laguerre diagram. We prove the convergence with linear speed of a damped Newton's algorithm to solve this non-linear system. The convergence relies on two conditions: (i) a genericity condition on the point cloud with respect to the simplex soup and (ii) a (strong) connectedness condition on the support of the source measure defined on the simplex soup. Finally, we apply our algorithm in R^3 to compute optimal transport plans between a measure supported on a triangulation and a discrete measure. We also detail some applications such as optimal quantization of a probability density over a surface, remeshing or rigid point set registration on a mesh.
Published: 2017
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9. Dopamine Modulates Motor Control in a Specific Plane Related to Support

Author: Lionel Reveret, Marc Herbin, Paul-Antoine Libourel, Daniel Eugène, J. Diaz, Rémi Hackert, Catherine de Waele, Caroline Simonis, Pierre-Paul Vidal, Muséum national d'Histoire naturelle (MNHN), Direction de l'évaluation, de la prospective et de la performance (DEPP), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Capture and Analysis of Shapes in Motion (MORPHEO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut National Polytechnique de Grenoble (INPG), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Centre de recherche en neurosciences de Lyon (CRNL), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université Paris Descartes - Paris 5 (UPD5), Institut de psychiatrie et neurosciences (U894 / UMS 1266), Université Paris Descartes - Paris 5 (UPD5)-Institut National de la Santé et de la Recherche Médicale (INSERM), Cognition and Action Group (COGNAC-G - UMR 8257), École normale supérieure - Cachan (ENS Cachan)-Université Paris Descartes - Paris 5 (UPD5)-Centre National de la Recherche Scientifique (CNRS), ANR-05-MMSA-0002,KAMELEON,Exploitation de masses de données anatomiques spatio-temporelles internes et externes denses pour l'étude des structures squelettiques des vertébrés(2005), Capture and Analysis of Shapes in Motion (MORPHEO ), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Mécanismes adaptatifs : des organismes aux communautés ( MAOAC ), Muséum National d'Histoire Naturelle ( MNHN ) -Collège de France ( CdF ) -Centre National de la Recherche Scientifique ( CNRS ), Direction de l'évaluation, de la prospective et de la performance ( DEPP ), Ministère de l'Éducation nationale, de l’Enseignement supérieur et de la Recherche ( M.E.N.E.S.R. ), Calcul des Variations, Géométrie, Image ( CVGI ), Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Laboratoire de Neurobiologie des Réseaux Sensorimoteurs ( LNRS ), Université Paris Diderot - Paris 7 ( UPD7 ) -Université Paris Descartes - Paris 5 ( UPD5 ), Centre de Psychiatrie et Neurosciences ( CPN - U894 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National de la Santé et de la Recherche Médicale ( INSERM ), Neurobiologie des réseaux sensorimoteurs ( NRS (U7060) ), Université Paris Diderot - Paris 7 ( UPD7 ) -Université Paris Descartes - Paris 5 ( UPD5 ) -Centre National de la Recherche Scientifique ( CNRS ), ANR-05-MMSA-0002,KAMELEON,Exploitation de masses de données anatomiques spatio-temporelles internes et externes denses pour l'étude des structures squelettiques des vertébrés ( 2005 ), Centre de recherche en neurosciences de Lyon - Lyon Neuroscience Research Center (CRNL), Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), and Centre de Psychiatrie et Neurosciences (U894)
Subjects: Male, 0301 basic medicine, Physiology, Dopamine, [SDV.NEU.NB]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, lcsh:Medicine, Biochemistry, Catecholamines, 0302 clinical medicine, Animal Cells, Mesencephalon, Medicine and Health Sciences, Homeostasis, Biomechanics, Amines, Animal Anatomy, lcsh:Science, Musculoskeletal System, Mammals, Neurons, Vestibular system, Multidisciplinary, Organic Compounds, [SDV.BA]Life Sciences [q-bio]/Animal biology, Dopaminergic, Neurochemistry, Animal Models, Neurotransmitters, Anatomy, Chemistry, [ SDV.NEU.NB ] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Neurobiology, Vertebrates, Physical Sciences, Neurochemicals, Cellular Types, medicine.symptom, Locomotion, Research Article, Biogenic Amines, Cognitive Neuroscience, Posture, Motor Activity, Research and Analysis Methods, Rodents, Lesion, Midbrain, Motor Reactions, 03 medical and health sciences, Model Organisms, Motor system, medicine, Animals, Rats, Wistar, Hydroxydopamine, Proprioception, Biological Locomotion, business.industry, Dopaminergic Neurons, lcsh:R, Organic Chemistry, Organisms, Chemical Compounds, Biology and Life Sciences, Motor control, Cell Biology, Hormones, Rats, Postural Control, 030104 developmental biology, Cellular Neuroscience, Amniotes, Cognitive Science, lcsh:Q, business, Dopaminergics, Zoology, 030217 neurology & neurosurgery, Neuroscience
Abstract: International audience; At the acute stage following unilateral labyrinthectomy (UL), rats, mice or guinea pigs exhibit a complex motor syndrome combining circling (HSCC lesion) and rolling (utricular lesion). At the chronic stage, they only display circling, because proprioceptive information related to the plane of support substitutes the missing utricular information to control posture in the frontal plane. Circling is also observed following unilateral lesion of the mesencephalic dopaminergic neurons by 6- hydroxydopamine hydrobromide (6-OHDA rats) and systemic injection of apomorphine (APO rats). The resemblance of behavior induced by unilateral vestibular and dopaminergic lesions at the chronic stage can be interpreted in two ways. One hypothesis is that the dopaminergic system exerts three-dimensional control over motricity, as the vestibular system does. If this hypothesis is correct, then a unilateral lesion of the nigro-striatal pathway should induce three-dimensional motor deficits, i.e., circling and at least some sort of barrel rolling at the acute stage of the lesion. Then, compensation could also take place very rapidly based on proprioception, which would explain the prevalence of circling. In addition, barrel rolling should reappear when the rodent is placed in water, as it occurs in UL vertebrates. Alternatively, the dopaminergic network, together with neurons processing the horizontal canal information, could control the homeostasis of posture and locomotion specifically in one and only one plane of space, i.e. the plane related to the basis of support. In that case, barrel rolling should never occur, whether at the acute or chronic stage on firm ground or in water. Moreover, circling should have the same characteristics following both types of lesions. Clearly, 6-OHDA and APO-rats never exhibited barrel rolling at the acute stage. They circled at the acute stage of the lesion and continued to do so three weeks later, including in water. In contrast, UL-rats, exhibited both circling and barrel rolling at the acute stage, and then only circled on the ground. Furthermore, barrel rolling instantaneously reappeared in water in UL rats, which was not the case in 6-OHDA and APO-rats. That is, the lesion of the dopaminergic system on one side did not compromise trim in the pitch and roll planes, even when proprioceptive information related to the basis of support was lacking as in water. Altogether, these results strongly suggest that dopamine does not exert three-dimensional control of the motor system but regulates postural control in one particular plane of space, the one related to the basis of support. In contrast, as previously shown, the vestibular system exerts three-dimensional control on posture. That is, we show here for the first time a relationship between a given neuromodulator and the spatial organization of motor control.
Published: 2016
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10. Une méthode d'optimisation pour l'appariement de formes élastiques

Author: de Buhan , Maya, Dapogny , Charles, Frey , Pascal, Nardoni , Chiara, Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Université Paris Descartes - Paris 5 (UPD5)-Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut des Sciences du Calcul et des Données (ISCD), Université Pierre et Marie Curie - Paris 6 (UPMC)-Sorbonne Université (SU), Université Pierre et Marie Curie - Paris 6 (UPMC), MAP5 - Mathématiques Appliquées à Paris 5 (MAP5), Université Paris Descartes - Paris 5 (UPD5) - Institut National des Sciences Mathématiques et de leurs Interactions - Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF) - Université Joseph Fourier - Grenoble 1 (UJF) - Institut Polytechnique de Grenoble - Grenoble Institute of Technology - Centre National de la Recherche Scientifique (CNRS) - Université Grenoble Alpes (UGA), Institut du Calcul et de la Simulation (ICS), Calcul des Variations, Géométrie, Image (CVGI), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Sorbonne Universités, Mathématiques Appliquées à Paris 5 ( MAP5 - UMR 8145 ), Université Paris Descartes - Paris 5 ( UPD5 ) -Institut National des Sciences Mathématiques et de leurs Interactions-Centre National de la Recherche Scientifique ( CNRS ), Calcul des Variations, Géométrie, Image ( CVGI ), Laboratoire Jean Kuntzmann ( LJK ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Institut du Calcul et de la Simulation ( ICS ), and Université Pierre et Marie Curie - Paris 6 ( UPMC )
Subjects: [ MATH ] Mathematics [math], [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: International audience; This note addresses the following shape matching problem: given a ‘template’ shape, numerically described by means of a computational mesh, and a ‘target’ shape, known only via a signed distance function to its boundary, we aim at deforming iteratively the mesh of the template shape into a computational mesh of the target shape. To achieve this goal, we rely on techniques from shape optimization. Under the sole assumption that both shapes share the same topology, the desired transformation is realized as a sequence of elastic displacements, which are obtained by minimizing an energy functional based on the distance between the two shapes. The proposed method has been implemented in a finite elements setting and numerical examples in two and three dimensions are presented to illustrate its efficiency.; Dans cette note, nous nous intéressons au problème d'appariement de formes suivant : étant donné une forme de référence, représentée numériquement par un maillage de calcul, et une forme cible, connue seulement par l'intermédiaire de la fonction de distance signée à celle-ci, notre objectif consiste à déformer itérativement le maillage de la forme de référence en un maillage de la forme cible. Pour ce faire, nous nous appuyons sur des techniques d'optimisation de formes. Sous l'hypothèse que les deux formes ont la même topologie, la transformation cherchée s'obtient comme une suite de déplacements élastiques, solutions d'un problème de minimisation d'une énergie basée sur la distance entre les formes. La méthode a été implémentée en deux et trois dimensions d'espace et nous présentons des exemples numériques permettant d'apprécier son efficacité.
Published: 2016
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11. Measuring the misfit between seismograms using an optimal transport distance: application to full waveform inversion

Author: Ludovic Métivier, Jean Virieux, Romain Brossier, Edouard Oudet, Quentin Mérigot, Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Institut des Sciences de la Terre (ISTerre), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-PRES Université de Grenoble-Institut de recherche pour le développement [IRD] : UR219-Institut national des sciences de l'Univers (INSU - CNRS)-Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Université Joseph Fourier - Grenoble 1 (UJF), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Calcul des Variations, Géométrie, Image (CVGI), Equations aux Dérivées Partielles (EDP ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut Français des Sciences et Technologies des Transports, de l'Aménagement et des Réseaux (IFSTTAR)-Institut national des sciences de l'Univers (INSU - CNRS)-Institut de recherche pour le développement [IRD] : UR219-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Calcul des Variations, Géométrie, Image (CVGI ), This study was partially funded by the SEISCOPE consortium (http://seiscope2.osug.fr), sponsored by BP, CGG, CHEVRON, EXXON-MOBIL, JGI, PETROBRAS, SAUDI ARAMCO, SCHLUMBERGER, SHELL, SINOPEC, STATOIL, TOTAL and WOODSIDE. This study was granted access to the HPC resources of the Froggy platform of the CIMENT infrastructure (https://ciment.ujf-grenoble.fr), which is supported by the Rhône- Alpes region (GRANT CPER07_13 CIRA), the OSUG@2020 labex (reference ANR-10-LABX-56) and the Equip@Meso project(reference ANR-10-EQPX-0029) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, and the HPC resources of CINES/IDRIS under the allocation 046091 made by GENCI., ANR-10-LABX-0056,OSUG@2020,Innovative strategies for observing and modelling natural systems(2010), ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris
Subjects: Mathematical optimization, Wave propagation, 010504 meteorology & atmospheric sciences, Computer science, Computation, Inversion (meteorology), [PHYS.PHYS.PHYS-GEO-PH]Physics [physics]/Physics [physics]/Geophysics [physics.geo-ph], Numerical approximation and analysis, 010502 geochemistry & geophysics, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computational seismology, Continuation, Geophysics, Seismic trace, Controlled source seismology, Geochemistry and Petrology, Benchmark data, Inverse theory, Seismogram, Algorithm, Full waveform, 0105 earth and related environmental sciences
Abstract: International audience; Full waveform inversion using the conventional $L^2$ distance to measure the misfit between seismograms is known to suffer from cycle skipping. An alternative strategy is proposed in this study, based on a measure of the misfit computed with an optimal transport distance. This measure allows to account for the lateral coherency of events within the seismograms, instead of considering each seismic trace independently, as is done generally in full waveform inversion. The computation of this optimal transport distance relies on a particular mathematical formulation allowing for the non-conservation of the total energy between seismograms. The numerical solution of the optimal transport problem is performed using proximal splitting techniques. Three synthetic case studies are investigated using this strategy: the Marmousi 2 model, the BP 2004 salt model, and the Chevron 2014 benchmark data. The results emphasize interesting properties of the optimal transport distance. The associated misfit function is less prone to cycle skipping. A workflow is designed to reconstruct accurately the salt structures in the BP 2004 model, starting from an initial model containing no information about these structures. A high-resolution $P$-wave velocity estimation is built from the Chevron 2014 benchmark data, following a frequency continuation strategy. This estimation explains accurately the data. Using the same workflow, full waveform inversion based on the $L^2$ distance converges towards a local minimum. These results yield encouraging perspectives regarding the use of the optimal transport distance for full waveform inversion: the sensitivity to the accuracy of the initial model is reduced, the reconstruction of complex salt structure is made possible, the method is robust to noise, and the interpretation of seismic data dominated by reflections is enhanced.
Published: 2016
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12. Automatic Estimation of Center of Mass from Multi-Camera Video System

Author: Goyallon, Thibault, Lahkar, Bhrigu, Marrec, Pierre, Dumas, Raphaël, Reveret, Lionel, Muller, Antoine, Robert, Thomas, Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon, Laboratoire de Biomécanique et Mécanique des Chocs (LBMC UMR T9406 ), Université de Lyon-Université de Lyon-Université Gustave Eiffel, and ANR-20-STHP-0003,PERFANALYTICS,Analyse in situ de la performance(2020)
Subjects: [SPI]Engineering Sciences [physics], [INFO]Computer Science [cs]
Abstract: International audience
Published: 2023

13. 'Conception et évaluation d’une méthode biomécaniquement cohérente d’analyse cinématique du geste sportif sans marqueur

Author: Pagnon, David, Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Université Grenoble Alpes [2020-....], Lionel Reveret, Calcul des Variations, Géométrie, Image (CVGI), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes, and Mathieu Domalain
Subjects: [INFO.INFO-AR]Computer Science [cs]/Hardware Architecture [cs.AR], MESH: Kinematics, Kinematics, Analyse de la performance sportive, Capture de mouvement Mocap, Cinématique, MESH: Markerless, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Python package, Capture de mouvement sans marqueurs, OpenPose, analyse de performance sportive, ACM: D.: Software/D.2: SOFTWARE ENGINEERING/D.2.4: Software/Program Verification/D.2.4.8: Validation, Vision par ordinateur, Package python, Markerless motion capture, Computer vision, Sports performance analysis, OpenSim, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph]
Abstract: Motion capture is traditionally performed with marker-based systems. However, these solutions are hardly compatible with on-field sports analysis, and markerless alternatives are being explored. One of the most promising prospects lies at the intersection of machine learning for 2D pose estimation, computer vision for 3D reconstruction from multiple video sources, and biomechanics for constraining 3D coordinates to an anatomically consistent model. We released Pose2Sim, an open-source package striving to answer these needs in a user-friendly way. OpenPose 2D keypoint coordinates are robustly triangulated, and serve as input for a full-body OpenSim inverse kinematics procedure. Pose2Sim robustness has been evaluated for people entering and exiting the field of view, degraded image quality, calibration errors, and decreased number of cameras. Its accuracy has also been assessed and deemed sufficient for walking, running, and ergometer cycling analysis. In the context of a competition, using lightweight and wireless action cameras is convenient. We tested such hardware on boxing sequences and proposed post-calibration and post-synchronization procedures. Finally, capturing both the athlete and their equipment can be valuable. We studied the kinematics of both a pilot and his bike in a BMX race by training a DeepLabCut bike model, triangulated and mapped on a custom-articulated OpenSim model. This work brings out interesting new perspectives for the analysis of sports movement.; La capture de mouvement est traditionnellement effectuée à l’aide de marqueurs réfléchissants placés sur la peau. Cependant, ces méthodes ne conviennent pas à l'analyse contextuelle du sport sur le terrain, et des alternatives sans marqueur sont étudiées. L’une des perspectives les plus prometteuses à ce sujet se situe à l’intersection de l’apprentissage machine pour l’estimation de pose 2D, de la vision par ordinateur pour la reconstruction 3D à partir de plusieurs sources vidéo, et de la biomécanique pour contraindre les coordonnées 3D à un modèle anatomiquement cohérent. Nous avons proposé Pose2Sim, un package open-source et simple d’utilisation visant à répondre à ces besoins. Les détections 2D d’OpenPose sont triangulées de manière robuste, et transmises à OpenSim pour une cinématique inverse corps complet. La robustesse de Pose2Sim a été estimée face à des personnes "parasites" entrant le champ de vision, à une qualité d’image dégradée, à des erreurs de calibration, et à un nombre de caméras réduit. Son exactitude a également été évaluée, et jugée satisfaisante pour l’analyse de la marche, de la course, et du cyclisme. Dans un contexte de compétition, il peut être utile d'employer des caméras légères et sans fil de type GoPro. Nous avons testé ce matériel sur des séquences de boxe, et proposé des procédures de post-calibration et de post-synchronisation. Enfin, capturer à la fois l’athlète et son équipement serait intéressant. Nous avons calculé la cinématique d’un pilote de BMX avec son vélo, en entraînant un modèle DeepLabCut pour le vélo, triangulé et appliqué sur un modèle poly-articulé OpenSim. L’ensemble de ces résultats apporte des perspectives novatrices pour l’analyse du mouvement sportif.
Published: 2023

14. The topological ligament in shape optimization: a connection with thin tubular inhomogeneities

Author: Dapogny, Charles, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Equations aux Dérivées Partielles (EDP)
Subjects: Statistics and Probability, Computational Mathematics, Numerical Analysis, Modeling and Simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: International audience; In this article, we propose a formal method for evaluating the asymptotic behavior of a shape functional when a thin tubular ligament is added between two distant regions of the boundary of a domain. In the contexts of the conductivity equation and the linear elasticity system, we relate this issue to a perhaps more classical problem of thin tubular inhomogeneities: we analyze the solutions to versions of the physical partial differential equations which are posed inside a fixed "background" medium, and whose material coefficients are altered inside a tube with vanishing thickness. Our main contribution from the theoretical point of view is to propose a heuristic energy argument to calculate the limiting behavior of these solutions with a minimum amount of effort. We retrieve known formulas when they are available, and we manage to treat situations which are, to the best of our knowledge, not reported in the literature (including the setting of the 3d linear elasticity system). From the numerical point of view, we propose three different applications of the formal "topological ligament" approach derived from these expansions. At first, it is an original way to account for variations of a domain, and it thereby provides a new type of sensitivity for a shape functional, to be used concurrently with more classical shape and topological derivatives in optimal design frameworks. Besides, it suggests new, interesting algorithms for the design of the scaffold structure sustaining a shape during its fabrication by a 3d printing technique, and for the design of truss-like structures. Several numerical examples are presented in two and three space dimensions to appraise the efficiency of these methods.
Published: 2022
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15. Pose2Sim: An open-source Python package for multiview markerless kinematics

Author: Mathieu Domalain, Lionel Reveret, David Pagnon, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Institut Pprime (PPRIME), and Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)
Subjects: [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph]
Abstract: International audience; Two-dimensional deep-learning pose estimation algorithms can suffer from biases in joint pose localizations, which are reflected in triangulated coordinates, and then in 3D joint angle estimation. Pose2Sim, our robust markerless kinematics workflow, comes with a physically consistent OpenSim skeletal model, meant to mitigate these errors. Its accuracy was concurrently validated against a reference marker-based method. Lower-limb joint angles were estimated over three tasks (walking, running, and cycling) performed multiple times by one participant. When averaged over all joint angles, the coefficient of multiple correlation (CMC) remained above 0.9 in the sagittal plane, except for the hip in running, which suffered from a systematic 15° offset (CMC = 0.65), and for the ankle in cycling, which was partially occluded (CMC = 0.75). When averaged over all joint angles and all degrees of freedom, mean errors were 3.0°, 4.1°, and 4.0°, in walking, running, and cycling, respectively; and range of motion errors were 2.7°, 2.3°, and 4.3°, respectively. Given the magnitude of error traditionally reported in joint angles computed from a marker-based optoelectronic system, Pose2Sim is deemed accurate enough for the analysis of lower-body kinematics in walking, cycling, and running.
Published: 2022
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16. A 3D markerless protocol with action cameras - Key performance indicators in boxing

Author: Pagnon, David, Domalain, Mathieu, Robert, Thomas, Lahkar, Bhrigu-Kumar, Moussa, Issa, Saulière, Guillaume, Goyallon, Thibault, Reveret, Lionel, Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire de Biomécanique et Mécanique des Chocs (LBMC UMR T9406 ), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Gustave Eiffel, and Institut national du sport, de l'expertise et de la performance (INSEP)
Subjects: [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], [SHS.SPORT.ITS]Humanities and Social Sciences/Sport/Sport engineering and technology
Abstract: International audience; Introduction:Marker-based kinematics is hardly compatible with sports movement analysis, especially because it hinders natural movement. Hence, deep-learning based markerless solutions are being developed, such as Pose2Sim [1]. Sports in competition may also be subject to setup constraints, preventing the use of heavy equipment and installation. The use of lightweight action cameras, with post-calibration and post-synchronization, can be pertinent in this context. This study aimed at investigating the accuracy of the Pose2Sim pipeline in such suboptimal conditions. We assessed the measures of key performance indicators in boxing, which involves swift and 3-dimensional full-body movements.Methods:One male elite boxer performed 6 repetitions of a boxing sequence composed of 3 punches (jab, high hook, low hook). His 3D motion was captured both with a marker-based protocol, and with a light-weight markerless one. The latter involved 8 GoPro cameras, which were post-calibrated based on the dimensions of the boxing ring, and post-synchronized based on time-lagged correlations of 2D keypoints speeds between paired cameras. The markerless kinematic analysis was then performed with Pose2Sim. Both protocols used the same OpenSim [2] model to optimize inverse kinematics. Displacement of lead foot, pelvis, lead fist, and velocity of lead fist were analyzed for the jab. Rotation of rear foot, pelvis, displacement of rear fist, and velocity of rear fist were analyzed for the hooks. Waveform similarity was assessed with the inter-protocol coefficient of multiple correlation [3]. Time and magnitude of peaks were also compared.Results:Results from the marker-based and markerless approaches demonstrated excellent waveform similarity (CMC>0.94), and times-to-peak exhibited intervals of under one frame (i.e., 17 ms). Magnitudes-at-peak were very close for displacements (below 6 cm), but not for fist velocity on jab (1.2m/s difference) nor for rotations on hooks (up to 20° difference, e.g. for pelvis rotation).Conclusion:Despite the use of action cameras, and of suboptimal calibration and synchronization procedures, our lightweight markerless protocol gives satisfying results for the analysis of key performance indicators in boxing, especially for limb displacements. Nevertheless, results should be taken with caution for velocity and for rotation measurements. Such a light-weight markerless protocol could be useful in situations where more accurate marker-based approaches are not conceivable, such as sports competitions.
Published: 2022

17. Shape and topology optimization for maximum probability domains in quantum chemistry

Author: Braida, Benoît, Dalphin, Jérémy, Dapogny, Charles, Frey, Pascal, Privat, Yannick, Laboratoire de chimie théorique (LCT), Institut de Chimie du CNRS (INC)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences du Calcul et des Données (ISCD), Sorbonne Université (SU), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), TOkamaks and NUmerical Simulations (TONUS), Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), The work of Charles Dapogny and Yannick Privat is partly supported by the project ANR-18-CE40-0013 SHAPO, financed by the French Agence Nationale de la Recherche (ANR)., ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018), Calcul des Variations, Géométrie, Image (CVGI), Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)-Inria Nancy - Grand Est, and Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA)
Subjects: Computational Mathematics, Maximum Probability Domains, AMS classification: 35P20, 93B07, 58J51, 49K20, Applied Mathematics, Fixed Point Algorithm, Shape Optimization, Level Set Method, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Quantum Chemistry
Abstract: International audience; This article is devoted to the mathematical and numerical treatments of a shape optimization problem emanating from the desire to reconcile quantum theories of chemistry and classical heuristic models: we aim to identify Maximum Probability Domains (MPDs), that is, domains $\Omega$ of the 3d space where the probability $\mathbb{P}_\nu(\Omega)$ to find exactly $\nu$ among the $n$ constituent electrons of a given molecule is maximum. In the Hartree-Fock framework, the shape functional $\mathbb{P}_\nu(\Omega)$ arises as the integral over $\nu$ copies of $\Omega$ and $(n-\nu)$ copies of the complement $\mathbb{R}^3 \setminus \Omega$ of an analytic function defined over the space $\mathbb{R}^{3n}$ of all the spatial configurations of the $n$ electron system. Our first task is to explore the mathematical well-posedness of the shape optimization problem: under mild hypotheses, we prove that global maximizers of the probability functions $\mathbb{P}_\nu(\Omega)$ do exist as open subsets of $\mathbb{R}^3$; meanwhile, we identify the associated necessary first-order optimality condition. We then turn to the numerical calculation of MPDs, for which we resort to a level set based mesh evolution strategy: the latter allows for the robust tracking of complex evolutions of shapes, while leaving the room for accurate chemical computations, carried out on high-resolution meshes of the optimized shapes. The efficiency of this procedure is enhanced thanks to the addition of a fixed-point strategy inspired from the first-order optimality conditions resulting from our theoretical considerations. Several three-dimensional examples are presented and discussed to appraise the efficiency of our algorithms.
Published: 2022
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18. Pose2Sim: An End-to-End Workflow for 3D Markerless Sports Kinematics-Part 2: Accuracy

Author: Mathieu Domalain, Lionel Reveret, David Pagnon, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Robotique, Biomécanique, Sport, Santé (RoBioSS), Département Génie Mécanique et Systèmes Complexes (GMSC), Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Institut Pprime (PPRIME), Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS)-Université de Poitiers-ENSMA-Centre National de la Recherche Scientifique (CNRS), and ANR-20-STHP-0003,PERFANALYTICS,Analyse in situ de la performance(2020)
Subjects: musculoskeletal diseases, Kinematics, Knee Joint, Sports performa, Walking, Biochemistry, Analytical Chemistry, Running, Workflow, OpenPose, Motion, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Humans, Electrical and Electronic Engineering, OpenSim, [PHYS.MECA.BIOM]Physics [physics]/Mechanics [physics]/Biomechanics [physics.med-ph], Instrumentation, Markerless moti, Gait, markerless motion capture, sports performance analysis, kinematics, computer vision, deep learning, concurrent validity, accuracy, [INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV], Deep learning, Atomic and Molecular Physics, and Optics, Biomechanical Phenomena, concurrent vali, Computer vision, Ankle Joint
Abstract: Two-dimensional deep-learning pose estimation algorithms can suffer from biases in joint pose localizations, which are reflected in triangulated coordinates, and then in 3D joint angle estimation. Pose2Sim, our robust markerless kinematics workflow, comes with a physically consistent OpenSim skeletal model, meant to mitigate these errors. Its accuracy was concurrently validated against a reference marker-based method. Lower-limb joint angles were estimated over three tasks (walking, running, and cycling) performed multiple times by one participant. When averaged over all joint angles, the coefficient of multiple correlation (CMC) remained above 0.9 in the sagittal plane, except for the hip in running, which suffered from a systematic 15° offset (CMC = 0.65), and for the ankle in cycling, which was partially occluded (CMC = 0.75). When averaged over all joint angles and all degrees of freedom, mean errors were 3.0°, 4.1°, and 4.0°, in walking, running, and cycling, respectively; and range of motion errors were 2.7°, 2.3°, and 4.3°, respectively. Given the magnitude of error traditionally reported in joint angles computed from a marker-based optoelectronic system, Pose2Sim is deemed accurate enough for the analysis of lower-body kinematics in walking, cycling, and running.
Published: 2022
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19. Blossoming and Hermite-Padé Approximation for Hypergeometric Series

Author: Marie-Laurence Mazure, Rachid Ait-Haddou, King Fahd University of Petroleum and Minerals (KFUPM), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Hermite polynomials, Series (mathematics), q-Blossoms, Applied Mathematics, Mathematics::Classical Analysis and ODEs, Hermite-Padé approximation, 010103 numerical & computational mathematics, 16. Peace & justice, 01 natural sciences, Hermite identity, Blossoms, Hypergeometric series, Exponential function, 010101 applied mathematics, Algebra, Identity (mathematics), Rational approximation, MSC: 65D17, 65D20, 41A20, 41A21, 41A28, Theory of computation, Padé approximant, 0101 mathematics, Hypergeometric function, [MATH]Mathematics [math], Binomial series, Mathematics
Abstract: International audience; Based on the blossoming theory, in this work we develop a new method for deriving Hermite-Padé approximants of certain hypergeometric series. Its general principle consists in building identities generalising the Hermite identity for exponentials, and in then applying their blossomed versions to appropriate tuples to simultaneously produce explicit expressions of the approximants and explicit integral representations of the corresponding remainders. For binomial series we use classical blossoms while for q-hypergeometric series we have to use q-blossoms.
Published: 2021
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20. Feature Lines Modification Based on As-Stiff-As-Needed Surface Deformation

Author: Youna Le Vaou, Matthieu Mika, Jean-Claude Léon, Stéphane Masfrand, Stefanie Hahmann, Authoring and directing story worlds (ANIMA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Groupe PSA - Centre Technique de Vélizy [Vélizy-Villacoublay]
Subjects: Surface (mathematics), physicalbased deformation, Computer science, Traction (engineering), Boundary (topology), Mechanical engineering, 02 engineering and technology, Deformation (meteorology), [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Industrial and Manufacturing Engineering, Computer aided design CAD, 0202 electrical engineering, electronic engineering, information engineering, Polygon mesh, ComputingMethodologies_COMPUTERGRAPHICS, 020207 software engineering, aesthetic design, Compression (physics), Computer Graphics and Computer-Aided Design, [INFO.INFO-GR]Computer Science [cs]/Graphics [cs.GR], 0104 chemical sciences, Computer Science Applications, 010404 medicinal & biomolecular chemistry, Feature (computer vision), feature lines, Line (geometry), mesh deformation
Abstract: International audience; Aesthetic surface mesh modification, guided by a deforming feature line, is still a challenging task. Whereas most existing surface deformation methods work well when the new surface is stretched or isometrically deformed, in case of areas subjected to compression, unwanted bulging may appear. This configuration typically appears when a designer slides a feature line along the input surface. In this paper, we present a new approach for feature line modification solving the surface bulging problem. We consider physically-based deformation methods applied to surface meshes and characterize configurations that produce compression loading from a mechanical standpoint. Then, the deformation area is decomposed into two sub-domains with a boundary modification of the one subjected to compression loading. Thus, during a subsequent deformation, this sub-domain no longer undergoes a compression loading but rather a traction loading, which ultimately prevents bulging. This transformation looks like a retraction of this surface area and a corresponding processing pipeline is set up. Our feature line modification method is intuitive to use and runs interactively, making it attractive to be used during design reviews in immersive environments. Industrial examples and comparisons with state-of-theart physically-based deformation methods validate the proposed approach.
Published: 2021
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21. Geometrically continuous piecewise Chebyshevian NU(R)BS

Author: Marie-Laurence Mazure, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: blossoms, Pure mathematics, rational splines, Computer Networks and Communications, Applied Mathematics, Identity matrix, geometric design, 010103 numerical & computational mathematics, 01 natural sciences, Chebyshev filter, Mathematics::Numerical Analysis, Piecewise Chebyshevian splines, 010101 applied mathematics, Computational Mathematics, Spline (mathematics), NURBS, Computer Science::Graphics, Piecewise, Equivalence relation, [MATH]Mathematics [math], 0101 mathematics, shape effects, Software, Mathematics
Abstract: International audience; By piecewise Chebyshevian splines we mean splines with pieces taken from different Extended Chebyshev spaces all of the same dimension, and with connection matrices at the knots. Within this very large and crucial class of splines, we are more specifically concerned with those which are good for design, in the sense that they possess blossoms, or, equivalently, refinable B-spline bases. In practice, this subclass is known to be characterised by the existence of (infinitely many) piecewise generalised derivatives with respect to which the continuity between consecutive pieces is controlled by identity matrices. Somehow inherent in the previous characterisation, the construction of all associated rational spline spaces creates an equivalence relation between piecewise Chebyshevian spline spaces good for design, among which the famous classical rational splines. We investigate this equivalence relation along with the natural question: Is it or not worthwhile considering the rational framework since it does not enlarge the set of resulting splines? This explains the parentheses inside the acronym NU(R)BS.
Published: 2020
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22. A connection between topological ligaments in shape optimization and thin tubular inhomogeneities

Author: Charles Dapogny, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Partial differential equation, General Mathematics, 010102 general mathematics, Mathematical analysis, Numerical Analysis (math.NA), Function (mathematics), 01 natural sciences, Domain (mathematical analysis), Connection (mathematics), Set (abstract data type), Optimization and Control (math.OC), 0103 physical sciences, FOS: Mathematics, Shape optimization, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Numerical Analysis, 010307 mathematical physics, Sensitivity (control systems), 0101 mathematics, Tube (container), Mathematics - Optimization and Control, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Mathematics
Abstract: International audience; In this note, we propose a formal framework accounting for the sensitivity of a function of the domain with respect to the addition of a thin ligament. To set ideas, we consider the model setting of elastic structures, and we approximate this question by a thin tubular inhomogeneity problem: we look for the sensitivity of the solution to a partial differential equation posed inside a background medium, and that of a related quantity of interest, with respect to the inclusion of a thin tube filled with a different material. A practical formula for this sensitivity is derived, which lends itself to numerical implementation. Two applications of this idea in structural optimization are presented.; Dans cette note, on introduit une approche formelle visant à évaluer la sensibilité d'une fonction du domaine par rapport à la greffe d'un ligament très fin sur celui-ci. Dans le contexte modèle des structures élastiques, nous approchons cette question par un problème de petite inclusion tubulaire : on étudie la sensibilité de la solution d'une équation aux dérivées partielles posée dans un milieu ambiant, ainsi que celle d'une quantité d'intérêt associée, par rapport à l'inclusion d'un tube fin contenant un matériau distinct de celui du milieu ambiant. On obtient une formule explicite pour cette sensibilité, qui se prête à l'implémentation numérique. Cette idée est illustrée par deux applications en optimisation structurale.
Published: 2020
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23. A variational formulation for computing shape derivatives of geometric constraints along rays

Author: Grégoire Allaire, Florian Feppon, Charles Dapogny, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Safran Tech, Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])
Subjects: Level set method, Discretization, Signed distance function, 010103 numerical & computational mathematics, Thickness constraints, Curvature, 01 natural sciences, Shape and topology optimization, signed distance function, Level set methods, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Shape optimization, 0101 mathematics, Mathematics, Numerical Analysis, AMS Subject classifications 65K10 , 49Q10, Applied Mathematics, Mathematical analysis, Finite element method, 010101 applied mathematics, Computational Mathematics, Variational method, Modeling and Simulation, Advection operator, Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], level set method, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis
Abstract: In the formulation of shape optimization problems, multiple geometric constraint functionals involve the signed distance function to the optimized shape Ω. The numerical evaluation of their shape derivatives requires to integrate some quantities along the normal rays to Ω, a challenging operation to implement, which is usually achieved thanks to the method of characteristics. The goal of the present paper is to propose an alternative, variational approach for this purpose. Our method amounts, in full generality, to compute integral quantities along the characteristic curves of a given velocity field without requiring the explicit knowledge of these curves on the spatial discretization; it rather relies on a variational problem which can be solved conveniently by the finite element method. The well-posedness of this problem is established thanks to a detailed analysis of weighted graph spaces of the advection operator β ⋅ ∇ associated to a C1 velocity field β. One novelty of our approach is the ability to handle velocity fields with possibly unbounded divergence: we do not assume div(β) ∈ L∞. Our working assumptions are fulfilled in the context of shape optimization of C2 domains Ω, where the velocity field β = ∇dΩ is an extension of the unit outward normal vector to the optimized shape. The efficiency of our variational method with respect to the direct integration of numerical quantities along rays is evaluated on several numerical examples. Classical albeit important implementation issues such as the calculation of a shape’s curvature and the detection of its skeleton are discussed. Finally, we demonstrate the convenience and potential of our method when it comes to enforcing maximum and minimum thickness constraints in structural shape optimization.
Published: 2020
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24. Phase-field modelling and computing for a large number of phases

Author: Jacques-Olivier Lachaud, Elie Bretin, Roland Denis, Edouard Oudet, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques (LAMA), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-11-BS02-0009,DigitalSnow,Géométrie discrète et mathématiques appliquées pour la métamorphose de neige(2011), ANR-15-CE40-0006,CoMeDiC,Métriques convergentes pour le calcul digital(2015), ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), ANR-11-IDEX-0007,Avenir L.S.E.,PROJET AVENIR LYON SAINT-ETIENNE(2011), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), and Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)
Subjects: Numerical Analysis, Mean curvature, Conjecture, Discretization, Applied Mathematics, Computation, Phase field models, 010103 numerical & computational mathematics, Non local, 01 natural sciences, multiphase perimeter, 010101 applied mathematics, MSC: 49Q05, 49Q20, 49M25, Computational Mathematics, Rate of convergence, kelvin conjecture, Modeling and Simulation, Partition (number theory), Phase-field model, 0101 mathematics, Algorithm, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis, Mathematics
Abstract: International audience; We propose a framework to represent a partition that evolves under mean curvature flows and volume constraints. Its principle follows a phase-field representation for each region of the partition, as well as classical Allen-Cahn equations for its evolution. We focus on the evolution and on the optimization of problems involving high resolution data with many regions in the partition. In this context, standard phase-field approaches require a lot of memory (one image per region) and computation timings increase at least as fast as the number of regions. We propose a more efficient storage strategy with a dedicated multi-image representation that retains only significant phase field values at each discretization point. We show that this strategy alone is unfortunately inefficient with classical phase field models. This is due to non local terms and low convergence rate. We therefore introduce and analyze an improved phase field model that localizes each phase field around its associated region, and which fully benefits of our storage strategy. To demonstrate the efficiency of the new multiphase field framework, we apply it to the famous 3D honeycomb problem and the conjecture of Weaire-Phelan's tiling.
Published: 2019
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25. Accelerated Directional Search with Non-Euclidean Prox-Structure

Author: Eduard Gorbunov, Evgeniya Vorontsova, Alexander Gasnikov, Calcul des Variations, Géométrie, Image (CVGI ), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Far Eastern Federal University (FEFU), and Moscow Institute of Physics and Technology [Moscow] (MIPT)
Subjects: 0209 industrial biotechnology, Mathematical optimization, convex optimization, Optimization problem, ускоренные методы первого порядка, Computer science, G.1.6, Structure (category theory), first-order accelerated methods, 02 engineering and technology, non-Euclidean prox-structure, 01 natural sciences, методлинейного каплинга, 020901 industrial engineering & automation, Non-Euclidean geometry, Euclidean geometry, FOS: Mathematics, Point (geometry), 0101 mathematics, Electrical and Electronic Engineering, linear coupling method, Mathematics - Optimization and Control, Descent (mathematics), 90C25, 90C30, 68Q25, 65K05, 65Y20, 68W40, 010102 general mathematics, концентрация равномерной меры на единичной евклидовойсфере, неевклидова прокс-структура, выпуклая оптимизация, Rate of convergence, Optimization and Control (math.OC), Control and Systems Engineering, Convex optimization, uniform measure concentration on a single Euclidean sphere, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: In the paper we propose an accelerated directional search method with non-euclidian prox-structure. We consider convex unconstraint optimization problem in $\mathbb{R}^n$. For simplicity we start from the zero point. We expect in advance that 1-norm of the solution is close enough to its 2-norm. In this case the standard accelerated Nesterov's directional search method can be improved. In the paper we show how to make Nesterov's method $n$-times faster (up to a $\log n$-factor) in this case. The basic idea is to use linear coupling, proposed by Allen-Zhu & Orecchia in 2014, and to make Grad-step in 2-norm, but Mirr-step in 1-norm. We show that for constrained optimization problems this approach stable upon an obstacle., in Russian, 13 pages, 3 figures
Published: 2019
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26. Quantum Lorentz Degrees of Polynomials and a Pólya Theorem for Polynomials Positive on q-Lattices

Author: Marie-Laurence Mazure, Ron Goldman, Rachid Ait-Haddou, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Department of computer Science [Houston], Rice University [Houston], Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Pure mathematics, Lorentz transformation, Uniform convergence, Bézier curve, 010103 numerical & computational mathematics, 01 natural sciences, q-lattices, Piecewise linear function, symbols.namesake, quantum Pólya's theorems, Limit (mathematics), 0101 mathematics, [MATH]Mathematics [math], Mathematics, degree elevation, Numerical Analysis, Degree (graph theory), q-positivity, q-blossom, Applied Mathematics, Univariate, q-Bernstein basis, 010101 applied mathematics, Computational Mathematics, Polygon, symbols, quantum Lorentz degrees
Abstract: We establish the uniform convergence of the control polygons generated by repeated degree elevation of q-Bezier curves (i.e., polynomial curves represented in the q-Bernstein bases of increasing degrees) on [ 0 , 1 ] , q > 1 , to a piecewise linear curve with vertices on the original curve. A similar result is proved for q 1 , but surprisingly the limit vertices are not on the original curve, but on the q − 1 -Bezier curve with control polygon taken in the reverse order. We introduce a q-deformation (quantum Lorentz degree) of the classical notion of Lorentz degree for polynomials and we study its properties. As an application of our convergence results, we introduce a notion of q-positivity which guarantees that the q-Lorentz degree is finite. We also obtain upper bounds for the quantum Lorentz degrees. Finally, as a by-product we provide a generalization to polynomials positive on q-lattices of the univariate Polya theorem concerning polynomials positive on the non-negative axis.
Published: 2021
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27. Formation tracking of target moving on natural surfaces

Author: H. Nadour, Pierre Legreneur, Lionel Reveret, Nicolas Marchand, GIPSA - COntrol, PErception, Robots, navigation and Intelligent Computing (GIPSA-COPERNIC), GIPSA Pôle Sciences des Données (GIPSA-PSD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Laboratoire Interuniversitaire de Biologie de la Motricité (LIBM ), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), AirCap Regional project funded by French ARA Region, Capture and Analysis of Shapes in Motion (MORPHEO), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), and Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])
Subjects: Computer science, Real-time computing, 3D reconstruction, Swarm behaviour, UAVs control, Solid modeling, formation control, Collision, Tracking (particle physics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Sight, monitoring, Position (vector), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, surveillance, target track-ing, Focus (optics), target tracking, film-making
Abstract: International audience; In this paper, we focus mainly on formation control of a swarm of UAV's tracking a moving target on a non regular mountainous surface. The main objective is to show how to dispatch the whole swarm of the quadrotors around the target (climber) with respect to the natural environment (mountain) taking advantage as much as possible from the free space surrounding the climber. The formation shape adapts with the neighbour environment topology, so that it avoids the collision with the environment and the concealing of the target from the UAV's cameras sights, and ensures as well the formation compactness and its closure to the target respecting the agent-agent and the agent-target security distances. The algorithm to define the free and safe hovering space (SHS) is then demonstrated with other two-steps algorithm to determine for each agent its desired position within the SHS. This work, that is considered as an introduction for upcoming works, does not miss to provide a simple control for each individual agent based on an established and corrected approximate dynamic model. The main idea to resolve this problem is explained in 2D and will be expanded for 3D environment, with other necessary and complementary enhancements. Keywords: UAVs control, formation control, target tracking, surveillance, film-making, 3D reconstruction, monitoring, quadrotor modeling.
Published: 2021
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28. A Novel Ridge Detector for Nonstationary Multicomponent Signals: Development and Application to Robust Mode Retrieval

Author: Nils Laurent, Sylvain Meignen, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and ANR-19-CE48-0001,ASCETE,Analyse et Séparation des signaux Complexes: Exploiter la structure Temps-fréquence(2019)
Subjects: Signal Processing (eess.SP), geography, geography.geographical_feature_category, Noise measurement, Computer science, Detector, Mode retrieval, 020206 networking & telecommunications, 02 engineering and technology, AM/FM multicomponent signals, Time–frequency analysis, Ridge detection, Noise, Ridge, Signal Processing, FOS: Electrical engineering, electronic engineering, information engineering, 0202 electrical engineering, electronic engineering, information engineering, Chirp, Short-time Fourier transform, Electrical and Electronic Engineering, Electrical Engineering and Systems Science - Signal Processing, Algorithm, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Continuous wavelet transform
Abstract: International audience; Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify their constituent modes. This is often done by performing ridge detection in the time-frequency plane which is then followed by mode retrieval. Unfortunately, existing ridge detectors are often not enough robust to noise therefore hampering mode retrieval. In this paper, we therefore develop a novel approach to ridge detection and mode retrieval based on the analysis of the short-time Fourier transform of multicomponent signals in the presence of noise, which will prove to be much more robust than state-of-the-art methods based on the same time-frequency representation.
Published: 2021
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29. What Makes Parkour Unique? A Narrative Review Across Miscellaneous Academic Fields

Author: David Pagnon, Germain Faity, Galo Maldonado, Yann Daout, Sidney Grosprêtre, Pôle de Ressources et d’Expertise Sportive et Scientifique (PRESS ), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), EuroMov - Digital Health in Motion (Euromov DHM), IMT - MINES ALES (IMT - MINES ALES), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Montpellier (UM), Institut de Biomécanique Humaine Georges Charpak (IBHGC), Université Sorbonne Paris Nord-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), Laboratoire Culture, sport, santé, société - UFC (UR 4660) (C3S), Université de Franche-Comté (UFC), and Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)
Subjects: Male, Foot, SportRxiv|Sport and Exercise Studies|Outdoor Education, [SDV]Life Sciences [q-bio], bepress|Life Sciences|Kinesiology, Physical Therapy, Sports Therapy and Rehabilitation, SportRxiv|Sport and Exercise Studies|Sport Sociology, bepress|Life Sciences|Kinesiology|Biomechanics, Biomechanical Phenomena, Lower Extremity, SportRxiv|Sport and Exercise Science|Sport and Exercise Biomechanics, Athletes, SportRxiv|Sport and Exercise Science, bepress|Social and Behavioral Sciences, SportRxiv|Sport and Exercise Science|Sport and Exercise Physiology, SportRxiv|Sport and Exercise Studies, Humans, Female, Orthopedics and Sports Medicine, Exercise, bepress|Life Sciences|Physiology, Sports
Abstract: International audience; Parkour is a growing sport that mostly involves jumping, vaulting over obstacles, and climbing in a non-dedicated setting. The authors gathered all known relevant literature across miscellaneous academic fields in order to define parkour with regard to other sports disciplines. Parkour is a lifestyle sport, and as such provides an alternative to mainstream sports, away from strict rules, standardized settings, and necessary competitions. Traceurs (parkour adepts) consider the city as a playground and as an outlet for their creativity, but they also have a strong taste for hard and individualized challenges. They usually train on non-specific structures, at ground level. Although their social background is not clear, they are mostly young and male. Traceurs are stronger than recreational athletes, especially in eccentric exercises. However, their endurance skills may be below average. One of the core specificities of parkour is its precision constraint at landing, which turns a standing long jump into a precision jump, regulated in flight so as to prepare for landing. The running precision jump follows the same landing pattern, and its flight phase contrasts with long jump techniques. Injuries, which are not more frequent than in other sports, often occur at landing and to lower limb extremities. This risk is mitigated by targeting the landing area with the forefoot instead of letting the heel hit the ground like in gymnastics, or with rolling in order to dissipate the impact. Overall, parkour focuses on adaptability to new environments, which leads to specific techniques that have not yet been extensively addressed by the literature.
Published: 2021
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30. No-slip and Free-slip divergence-free wavelets in three and higher dimension for the simulation of incompressible viscous flows

Author: Kadri, Souleymane, Perrier, Valérie, La Rochelle Université (ULR), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), R. Deiterding, M.-O. Domingues, and K. Schneider
Subjects: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; This work concerns divergence-free wavelet based methods for the numerical resolution of Navier-Stokes equations. It generalizes to higher dimension the approach of [23] that reformulates the projection method using the Helmholtz-Hodge decomposition in wavelet domain. The solution is searched in a finite dimensional free-slip divergence-free wavelet space, with time-dependent wavelet coefficients. We prove and verify the convergence of a first-order time numerical scheme for the Helmholtz-Hodge based projection method. Numerical simulations on the 3D Lid driven cavity flow show the accuracy and efficiency of the method.
Published: 2021
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31. Morphological bases of phytoplankton energy management and physiological responses unveiled by 3D subcellular imaging

Author: Guy Schoehn, Clarisse Uwizeye, Gilles Curien, Rachel Templin, Samuel C. Zeeman, Yannick Schwab, Davide Dal Bo, Denis Falconet, Fabien Chevalier, Serena Flori, Christine Moriscot, Florence Courtois, Claire Seydoux, Jean-Baptiste Keck, Benoit Gallet, Johan Decelle, Nicole L. Schieber, Pierre-Henri Jouneau, Giovanni Finazzi, Guillaume Allorent, LIPID, Physiologie cellulaire et végétale (LPCV), Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Grenoble Alpes (UGA), Photosymbiose, Modélisation et Exploration des Matériaux (MEM), Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes (UGA), Light Photosynthesis & Metabolism (Photosynthesis), Institut de biologie structurale (IBS - UMR 5075), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Cell Biology and Cell Biophysics Unit, European Molecular Biology Laboratory, European Molecular Biology Laboratory [Grenoble] (EMBL), Department of Biology [ETH Zürich] (D-BIOL), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Défi X-Life grant from CNRS, CEA DRFimpulsion FIB-Bioprogram, Auvergne-Rhône-Alpes Region, Fondation Recherche Medicale (FRM), FEDER and the GIS-Infrastructures en Biologie Santé et Agronomie (IBiSA), ANR-10-LABX-0049,GRAL,Grenoble Alliance for Integrated Structural Cell Biology(2010), ANR-17-EURE-0003,CBH-EUR-GS,CBH-EUR-GS(2017), ANR-17-CE05-0029,MoMix,Modélisation de la Mixotrophie chez l'algue extrêmophile Galdieria sulphuraria(2017), ANR-10-INBS-0005,FRISBI,Infrastructure Française pour la Biologie Structurale Intégrée(2010), ANR-15-IDEX-0002,UGA,IDEX UGA(2015), European Project: 833184, ChloroMito, and European Project: 654248,H2020,H2020-INFRADEV-1-2014-1,CORBEL(2015)
Subjects: 0106 biological sciences, 0301 basic medicine, Cell biology, Light, Bioenergetics, MESH: Mitochondria, Acclimatization, Science, General Physics and Astronomy, MESH: Acclimatization, MESH: Imaging, Three-Dimensional, Cellular imaging, Photosynthesis, 01 natural sciences, Article, General Biochemistry, Genetics and Molecular Biology, Pyrenoid, MESH: Microalgae, 03 medical and health sciences, Imaging, Three-Dimensional, Phytoplankton, Microalgae, [SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology, Plastids, Plastid, Cellular microbiology, Trophic level, Biomass (ecology), Multidisciplinary, biology, Ecology, MESH: Energy Metabolism, fungi, MESH: Plastids, General Chemistry, biology.organism_classification, MESH: Light, Mitochondria, 030104 developmental biology, Diatom, MESH: Subcellular Fractions, Energy Metabolism, Subcellular Fractions, MESH: Phytoplankton, 010606 plant biology & botany
Abstract: Eukaryotic phytoplankton have a small global biomass but play major roles in primary production and climate. Despite improved understanding of phytoplankton diversity and evolution, we largely ignore the cellular bases of their environmental plasticity. By comparative 3D morphometric analysis across seven distant phytoplankton taxa, we observe constant volume occupancy by the main organelles and preserved volumetric ratios between plastids and mitochondria. We hypothesise that phytoplankton subcellular topology is modulated by energy-management constraints. Consistent with this, shifting the diatom Phaeodactylum from low to high light enhances photosynthesis and respiration, increases cell-volume occupancy by mitochondria and the plastid CO2-fixing pyrenoid, and boosts plastid-mitochondria contacts. Changes in organelle architectures and interactions also accompany Nannochloropsis acclimation to different trophic lifestyles, along with respiratory and photosynthetic responses. By revealing evolutionarily-conserved topologies of energy-managing organelles, and their role in phytoplankton acclimation, this work deciphers phytoplankton responses at subcellular scales., Nature Communications, 12 (1), ISSN:2041-1723
Published: 2021
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32. Double-diffusive sedimentation at high Schmidt numbers: Semi-Lagrangian simulations

Author: Georges-Henri Cottet, Jean-Baptiste Keck, Christophe Picard, Iraj Mortazavi, Eckart Meiburg, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles (EDP), University of California [Santa Barbara] (UC Santa Barbara), University of California (UC), Modélisation mathématique et numérique (M2N), Conservatoire National des Arts et Métiers [CNAM] (CNAM), 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), ANR-17-CE23-0024,MPARME,Méthodes particulaires multi-résolution pour la simulation d'écoulements multiphasiques(2017), ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), University of California [Santa Barbara] (UCSB), University of California, and ANR: 10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010)
Subjects: Fluid Flow and Transfer Processes, Physics, Scaling law, 010504 meteorology & atmospheric sciences, Sedimentation (water treatment), [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Schmidt number, Computational Mechanics, Mechanics, 01 natural sciences, 010305 fluids & plasmas, Physics::Fluid Dynamics, symbols.namesake, Modeling and Simulation, Scientific method, 0103 physical sciences, symbols, hysop, Lagrangian, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], 0105 earth and related environmental sciences, Dimensionless quantity
Abstract: International audience; When particle-laden freshwater is placed above clear saltwater, double-diffusive sedimentation can arise. Navier-Stokes direct numerical simulations by Burns and Meiburg showed that this process can be dominated by either Rayleigh-Taylor or double-diffusive fingering instabilities. Based on two-dimensional simulations, those authors identify a single dimensionless parameter that can be employed to distinguish between these regimes. Here we develop a high-performance semi-Lagrangian computational approach that enables us to extend these high Schmidt number simulations to three dimensions, and to confirm the validity of their proposed scaling law for three-dimensional flows.
Published: 2021
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33. A damped Newton algorithm for generated Jacobian equations

Author: Gallouët, Anatole, Merigot, Quentin, Thibert, Boris, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Université Grenoble Alpes, and Université Paris Sud
Subjects: [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: Generated Jacobian Equations have been introduced by Trudinger [Disc. cont. dyn. sys (2014), pp. 1663-1681] as a generalization of Monge-Ampère equations arising in optimal transport. In this paper, we introduce and study a damped Newton algorithm for solving these equations in the semi-discrete setting, meaning that one of the two measures involved in the problem is finitely supported and the other one is absolutely continuous. We also present a numerical application of this algorithm to the near-field parallel refractor problem arising in non-imaging problems.
Published: 2021

34. Inertial Measurement of Head Tilt in Rodents: Principles and Applications to Vestibular Research

Author: Pauline Liaudet, Lionel Reveret, Mathieu Petremann, Romain Fayat, Guillaume P. Dugué, Vincent Descossy, Viviana Delgado Betancourt, Thibault Goyallon, Dugué, Guillaume, Institut de biologie de l'ENS Paris (IBENS), Département de Biologie - ENS Paris, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Sensorion [Montpellier], Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), ANR-20-CE37-0016,InVest,Circuits vestibulo-cérébelleux impliqués dans la cognition spatiale(2020), Institut de biologie de l'ENS Paris (UMR 8197/1024) (IBENS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Département de Biologie - ENS Paris, École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Département de Biologie - ENS Paris
Subjects: Inertial frame of reference, Computer science, Movement, Acceleration, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, [SDV.NEU.PC] Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Psychology and behavior, unilateral vestibular lesion, Rodentia, TP1-1185, Biochemistry, Motion capture, Article, Analytical Chemistry, 03 medical and health sciences, 0302 clinical medicine, Inertial measurement unit, [SPI.MECA.BIOM] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], Animals, Computer vision, Electrical and Electronic Engineering, orientation filters, Instrumentation, 030304 developmental biology, Vestibular system, 0303 health sciences, Quantitative Biology::Neurons and Cognition, [SDV.NEU.PC]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC]/Psychology and behavior, Orientation (computer vision), business.industry, Chemical technology, head tilt, vestibular system, [SPI.MECA.BIOM]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Biomechanics [physics.med-ph], inertial sensors, attitude estimation, Atomic and Molecular Physics, and Optics, Rats, Tilt (optics), rodents, Computer Science::Programming Languages, Head (vessel), Vestibule, Labyrinth, Artificial intelligence, business, 030217 neurology & neurosurgery, Gravitation
Abstract: Inertial sensors are increasingly used in rodent research, in particular for estimating head orientation relative to gravity, or head tilt. Despite this growing interest, the accuracy of tilt estimates computed from rodent head inertial data has never been assessed. Using readily available inertial measurement units mounted onto the head of freely moving rats, we benchmarked a set of tilt estimation methods against concurrent 3D optical motion capture. We show that, while low-pass filtered head acceleration signals only provided reliable tilt estimates in static conditions, sensor calibration combined with an appropriate choice of orientation filter and parameters could yield average tilt estimation errors below 1.5∘ during movement. We then illustrate an application of inertial head tilt measurements in a preclinical rat model of unilateral vestibular lesion and propose a set of metrics describing the severity of associated postural and motor symptoms and the time course of recovery. We conclude that headborne inertial sensors are an attractive tool for quantitative rodent behavioral analysis in general and for the study of vestibulo-postural functions in particular.
Published: 2021
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35. Riesz-based orientation of localizable Gaussian fields

Author: Kévin Polisano, Valérie Perrier, Laurent Condat, Marianne Clausel, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), GIPSA Pôle Géométrie, Apprentissage, Information et Algorithmes (GIPSA-GAIA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )
Subjects: Field (physics), Gaussian, H-sssi fields, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, Structure tensor, structure tensor, 010104 statistics & probability, symbols.namesake, orientation vector, localizable fields, Tensor, 0101 mathematics, Eigenvalues and eigenvectors, Mathematics, Random field, Applied Mathematics, 010102 general mathematics, Mathematical analysis, Function (mathematics), Fractional fields, Orientation (vector space), Mathematics - Classical Analysis and ODEs, symbols, anisotropy function, Riesz analysis, tangent fields
Abstract: International audience; In this work we give a sense to the notion of orientation for self-similar Gaussian fields with stationary increments, based on a Riesz analysis of these fields, with isotropic zero-mean analysis functions. We propose a structure tensor formulation and provide an intrinsic definition of the orientation vector as eigenvector of this tensor. That is, we show that the orientation vector does not depend on the analysis function, but only on the anisotropy encoded in the spectral density of the field. Then, we generalize this definition to a larger class of random fields called localizable Gaussian fields, whose orientation is derived from the orientation of their tangent fields. Two classes of Gaussian models with prescribed orientation are studied in the light of these new analysis tools.
Published: 2021
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36. Indicateurs de suivi de l'activité scientifique de l'Inria

Author: Brotcorne, Luce, Canteaut, Anne, Viana, Aline, Grandmont, Céline, Guedj, Benjamin, Huot, Stéphane, Issarny, Valérie, Pallez, Guillaume, Perrier, Valérie, Quema, Vivien, Pomet, Jean-Baptiste, Rival, Xavier, Salvati, Sylvain, Thomé, Emmanuel, Integrated Optimization with Complex Structure (INOCS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université libre de Bruxelles (ULB)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), 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), inTeRnet BEyond the usual (TRiBE ), Inria Saclay - Ile de France, COmputational Mathematics for bio-MEDIcal Applications (COMMEDIA), 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), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Technology and knowledge for interaction (LOKI), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Middleware on the Move (MIMOVE), Topology-Aware System-Scale Data Management for High-Performance Computing (TADAAM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Laboratoire d'Informatique de Grenoble (LIG), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Mathematics for Control, Transport and Applications (McTAO), Inria Sophia Antipolis - Méditerranée (CRISAM), Analyse Statique par Interprétation Abstraite (ANTIQUE), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Linking Dynamic Data (LINKS), 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), Inria, 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), Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Inria Bordeaux - Sud-Ouest, Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris, Department of Algorithms, Computation, Image and Geometry (LORIA - ALGO), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria)-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 Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Canteaut, Anne
Subjects: [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], [MATH.MATH-HO] Mathematics [math]/History and Overview [math.HO], [INFO.INFO-GL]Computer Science [cs]/General Literature [cs.GL], [INFO.INFO-GL] Computer Science [cs]/General Literature [cs.GL]
Abstract: La Commission d'Evaluation de l'Inria a mis en place début 2020, à la demande de la Direction Générale, un groupe de travail visant à réfléchir à des indicateurs pour l'analyse qualitative de l'activité scientifique de l'Institut. Ce document est le fruit des discussions de ce groupe, enrichies par les échanges avec la Direction Générale d'Inria et avec l'ensemble de la Commision d'Evaluation. Au-delà de cette « commande », il nous a semblé important de saisir cette opportunité pour mener une réflexion collective, qui dépasse le cadre de notre Institut, sur les indicateurs, et sur ce qu'ils peuvent ou ne peuvent pas dire de nos pratiques scientifiques.
Published: 2020

37. Dimension elevation is not always corner-cutting

Author: Marie-Laurence Mazure, Carolina Vittoria Beccari, Giulio Casciola, Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Beccari C.V., Casciola G., and Mazure M.-L.
Subjects: Degree (graph theory), Basis (linear algebra), Applied Mathematics, 010102 general mathematics, corner cutting, Elevation, Extended Chebyshev spaces, Bernstein bases, Space (mathematics), Bernstein base, 01 natural sciences, 010101 applied mathematics, Combinatorics, Extended Chebyshev space, Transformation (function), Dimension (vector space), Embedding, 0101 mathematics, dimension elevation, [MATH]Mathematics [math], shape preservation, PSPACE, Mathematics, critical length
Abstract: International audience; Degree elevation is a typical corner-cutting algorithm. It refers to the process transforming control polygons when embedding a polynomial space of some degree into any polynomial space of higher degree.Dimension elevation similarly refers to the transformation of control polygons when embedding an Extended Chebyshev space possessing a Bernstein basis into another one, of higher dimension. Unlike degree elevation, this cannot always be split into successive (corner-cutting) steps elevating the dimension by one. What happens when it is not possible is investigated here. We shall see that the new control points can even be located outside the initial control polygons, giving evidence that dimension elevation is not always corner-cutting.
Published: 2020
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38. 3D Visualization of Body Motion in Speed Climbing

Author: Franck Quaine, Lionel Reveret, Pierre Legreneur, Sylvain Chapelle, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Fédération Française de la Montagne et de l'Escalade, GIPSA - Analyse et Modification de l'homme en mouvement : biomécanique, cognition, vocologie (GIPSA-MOVE), GIPSA Pôle Sciences des Données (GIPSA-PSD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Laboratoire Interuniversitaire de Biologie de la Motricité (LIBM ), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), and Université de Lyon-Université de Lyon-Université Jean Monnet - Saint-Étienne (UJM)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])
Subjects: Motion analysis, lcsh:BF1-990, Tracking (particle physics), biomechanics, 050105 experimental psychology, Motion (physics), [SPI]Engineering Sciences [physics], 03 medical and health sciences, 0302 clinical medicine, video analysis, Psychology, 0501 psychology and cognitive sciences, Computer vision, Polygon mesh, General Psychology, Original Research, Plane (geometry), business.industry, motion analysis, 05 social sciences, speed climbing, Visualization, lcsh:Psychology, 3D visualization, center of mass, Climbing, Artificial intelligence, business, 030217 neurology & neurosurgery, Energy (signal processing)
Abstract: International audience; Speed climbing involves an optimization of the velocity of the ascent and the trajectory path during performance. Consequently, any amount of energy spent in the two other directions than vertical, namely the lateral direction and the direction perpendicular to the wall plane, is a potential loss of performance. To assess this principle, we present a study on 3D motion analysis and its 3D visualization for a subject during a speed climbing performance. The fundamentals of geometrical measurement in 3D require to integrate multiple 2D cues, at least two, in order to extract 3D information. First results with two drones following an athlete's ascent show that a 3D velocity profile can be provided from the tracking of a marker on the harness, pointing critical phases in the ascent where the vertical speed is not dominant any more. We further investigate 3D motion of full body using markerless video-based tracking. Our approach is based on a full body 3D avatar model of the climber, represented as a 3D mesh. This model and its deformation are learned in a laboratory studio. The learning needs to be done only once. Result is a manifold embedding of the 3D mesh and its deformations, which can be used afterwards to perform registration onto video of performance of speed climbing. The results of the tracking is an inference of the 3D mesh aligned onto videos of speed climbing performance. From this 3D mesh, we deduce an estimation of the center of mass (COM). We show that this estimation from 3D mesh differs from the usual approximation of the COM as a marker on the harness. In particular, the 3D mesh COM takes into account the whole body movement such as the influence of the limbs which is not detected by a marker on the harness.
Published: 2020
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39. A Novel Approach for Ridge Detection and Mode Retrieval of Multicomponent Signals Based on STFT

Author: Laurent, Nils, Meignen, Sylvain, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Short-time Fourier transform, Mode retrieval, AM/FM multicomponent signals, [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing, Ridge detection
Abstract: Time-frequency analysis is often used to study non stationary multicomponent signals, which can be viewed as the surperimposition of modes, associated with ridges in the TF plane. To understand such signals, it is essential to identify their constituent modes. This is often done by performing ridge detection in the time-frequency plane which is then followed by mode retrieval. Unfortunately, existing ridge detectors are often not enough robust to noise therefore hampering mode retrieval. In this paper, we therefore develop a novel approach to ridge detection and mode retrieval based on the analysis of the short-time Fourier transform of multicomponent signals in the presence of noise, which will prove to be much more robust than state-of-the-art methods based on the same time-frequency representation.
Published: 2020

40. Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers

Author: Pierre Jolivet, Grégoire Allaire, Florian Feppon, Charles Dapogny, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....]), Algorithmes Parallèles et Optimisation (IRIT-APO), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées, Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Centre National de la Recherche Scientifique (CNRS), ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)
Subjects: Convective heat transfer, Discretization, geometric constraints, Computer science, Computational Mechanics, General Physics and Astronomy, 010103 numerical & computational mathematics, 01 natural sciences, Shape and topology optimization, Heat exchanger, heat exchangers, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Shape optimization, 0101 mathematics, Mechanical Engineering, Numerical analysis, Topology optimization, Mechanics, non-mixing constraint, Computer Science Applications, 010101 applied mathematics, Test case, convective heat transfer, Mechanics of Materials, Solid body, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; We present a topology optimization approach for the design of fluid-to-fluid heat exchangers which rests on an explicit meshed discretization of the phases at stake, at every iteration of the optimization process. The considered physical situations involve a weak coupling between the Navier-Stokes equations for the velocity and the pressure in the fluid, and the convection-diffusion equation for the temperature field. The proposed framework combines several recent techniques from the field of shape and topology optimization, and notably a level-set based mesh evolution algorithm for tracking shapes and their deformations , an efficient optimization algorithm for constrained shape optimization problems, and a numerical method to handle a wide variety of geometric constraints such as thickness constraints and non-penetration constraints. Our strategy is applied to the optimization of various types of heat exchangers. At first, we consider a simplified 2D cross-flow model where the optimized boundary is the section of the hot fluid phase flowing in the transverse direction, which is naturally composed of multiple holes. A minimum thickness constraint is imposed on the cross-section so as to account for manufacturing and maximum pressure drop constraints. In a second part, we optimize the design of 2D and 3D heat exchangers composed of two types of fluid channels (hot and cold), which are separated by a solid body. A non-mixing constraint between the fluid components containing the hot and cold phases is enforced by prescribing a minimum distance between them. Numerical results are presented on a variety of test cases, demonstrating the efficiency of our approach in generating new, realistic, and unconventional heat exchanger designs.
Published: 2020
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41. Optimization of the shape of regions supporting boundary conditions

Author: Nicolas Lebbe, Charles Dapogny, Edouard Oudet, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Laplace's equation, Pure mathematics, Partial differential equation, Applied Mathematics, Numerical analysis, 010103 numerical & computational mathematics, 01 natural sciences, Robin boundary condition, Dirichlet distribution, 010101 applied mathematics, Computational Mathematics, symbols.namesake, Hadamard transform, Neumann boundary condition, symbols, Boundary value problem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics
Abstract: This article deals with the optimization of the shape of the regions assigned to different types of boundary conditions in the definition of a ‘physical’ partial differential equation. At first, we analyze a model situation involving the solution $$u_\varOmega $$ to a Laplace equation in a domain $$\varOmega $$ ; the boundary $$\partial \varOmega $$ is divided into three parts $$\varGamma _D$$ , $$\varGamma $$ and $$\varGamma _N$$ , supporting respectively homogeneous Dirichlet, homogeneous Neumann and inhomogeneous Neumann boundary conditions. The shape derivative $$J^\prime (\varOmega )(\theta )$$ of a general objective function $$J(\varOmega )$$ of the domain is calculated in the framework of Hadamard’s method when the considered deformations $$\theta $$ are allowed to modify the geometry of $$\varGamma _D$$ , $$\varGamma $$ and $$\varGamma _N$$ (i.e. $$\theta $$ does not vanish on the boundary of these regions). The structure of this shape derivative turns out to depend very much on the regularity of $$u_\varOmega $$ near the boundaries of the regions $$\varGamma _D$$ , $$\varGamma $$ and $$\varGamma _N$$ . For this reason, in particular, $$J^\prime (\varOmega )$$ is difficult to calculate and to evaluate numerically when the transition $$\overline{\varGamma _D} \cap {\overline{\varGamma }}$$ between homogeneous Dirichlet and homogeneous Neumann boundary conditions is subject to optimization. To overcome this difficulty, an approximation method is proposed, in which the considered ‘exact’ Laplace equation with mixed boundary conditions is replaced with a ‘smoothed’ version, featuring Robin boundary conditions on the whole boundary $$\partial \varOmega $$ with coefficients depending on a small parameter $$\varepsilon $$ . We prove the consistency of this approach in our model context: the approximate objective function $$J_\varepsilon (\varOmega )$$ and its shape derivative converge to their exact counterparts as $$\varepsilon $$ vanishes. Although it is rigorously justified only in a model problem, this approximation methodology may be adapted to many more complex situations, for example in three space dimensions, or in the context of the linearized elasticity system. Various numerical examples are eventually presented in order to appraise the efficiency of the proposed approximation process.
Published: 2020
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42. Interpolated corrected curvature measures for polygonal surfaces

Author: Jacques-Olivier Lachaud, David Coeurjolly, Pascal Romon, Boris Thibert, Laboratoire de Mathématiques (LAMA), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Laboratoire Analyse et Mathématiques Appliquées (LAMA), Université Paris-Est Créteil Val-de-Marne - Paris 12 (UPEC UP12)-Centre National de la Recherche Scientifique (CNRS)-Université Gustave Eiffel, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Origami (Origami), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), and Université de Lyon-Université Lumière - Lyon 2 (UL2)
Subjects: Pointwise convergence, Current (mathematics), Mathematical analysis, 020207 software engineering, 02 engineering and technology, Computational geometry, Curvature, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], Computer Graphics and Computer-Aided Design, Grassmannian, [INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV], Normal mapping, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Polygon mesh, Ball (mathematics), Mathematics, ComputingMethodologies_COMPUTERGRAPHICS
Abstract: International audience; A consistent and yet practically accurate definition of curvature onto polyhedral meshes remains an open problem. We propose a new framework to define curvature measures, based on the Corrected Normal Current, which generalizes the normal cycle: it uncouples the positional information of the polyhedral mesh from its geometric normal vector field, and the user can freely choose the corrected normal vector field at vertices for curvature computations. A smooth surface is then built in the Grassmannian R3 × S2 by simply interpolating the given normal vector field. Curvature measures are then computed using the usual Lipschitz–Killing forms, and we provide closed-form formulas per triangle. We prove a stability result with respect to perturbations of positions and normals. Our approach provides a natural scale-space for all curvature estimations, where the scale is given by the radius of the measuring ball. We show on experiments how this method outperforms state-of-the-art methods on clean and noisy data, and even achieves pointwise convergence on difficult polyhedral meshes like digital surfaces. The framework is also well suited to curvature computations using normal map information.
Published: 2020
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43. Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems

Author: Edouard Oudet, Chiu-Yen Kao, Braxton Osting, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), University of California [Los Angeles] (UCLA), University of California, University of California (UC), and ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018)
Subjects: Mathematics - Differential Geometry, Control and Optimization, Boundary (topology), 01 natural sciences, eigenvalue optimization, Mathematics - Spectral Theory, Steklov eigenvalue, Genus (mathematics), free boundary minimal surface, FOS: Mathematics, Ball (mathematics), 0101 mathematics, [MATH]Mathematics [math], Spectral Theory (math.SP), Mathematics - Optimization and Control, Eigenvalues and eigenvectors, Mathematics, Minimal surface, 010102 general mathematics, Degenerate energy levels, Mathematical analysis, Eigenfunction, Mathematics::Spectral Theory, 16. Peace & justice, Surface (topology), 010101 applied mathematics, Computational Mathematics, Differential Geometry (math.DG), Optimization and Control (math.OC), Control and Systems Engineering, 35P05, 35P15, 49Q05, 65N25
Abstract: Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary minimal surface, i.e., a surface contained in the ball that has (i) zero mean curvature and (ii) meets the boundary of the ball orthogonally (doi:10.1007/s00222-015-0604-x). In this paper, we develop numerical methods that use this connection to realize free boundary minimal surfaces. Namely, on a compact surface, $\Sigma$, with genus $\gamma$ and $b$ boundary components, we maximize $\sigma_j(\Sigma,g) \ L(\partial \Sigma, g)$ over a class of smooth metrics, $g$, where $\sigma_j(\Sigma,g)$ is the $j$-th nonzero Steklov eigenvalue and $L(\partial \Sigma, g)$ is the length of $\partial \Sigma$. Our numerical method involves (i) using conformal uniformization of multiply connected domains to avoid explicit parameterization for the class of metrics, (ii) accurately solving a boundary-weighted Steklov eigenvalue problem in multi-connected domains, and (iii) developing gradient-based optimization methods for this non-smooth eigenvalue optimization problem. For genus $\gamma =0$ and $b=2,\dots, 9, 12, 15, 20$ boundary components, we numerically solve the extremal Steklov problem for the first eigenvalue. The corresponding eigenfunctions generate a free boundary minimal surface, which we display in striking images. For higher eigenvalues, numerical evidence suggests that the maximizers are degenerate, but we compute local maximizers for the second and third eigenvalues with $b=2$ boundary components and for the third and fifth eigenvalues with $b=3$ boundary components., Comment: 29 pages, 18 figures
Published: 2020
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44. In-cell quantitative structural imaging of phytoplankton using 3D electron microscopy

Author: Nicole L. Schieber, Gilles Curien, Rachel Templin, Johan Decelle, Jean-Baptiste Keck, Samuel C. Zeeman, Denis Falconet, Pierre-Henri Jouneau, Christine Moriscot, Guy Schoehn, Fabien Chevalier, Giovanni Finazzi, Clarisse Uwizeye, Benoit Gallet, Yannick Schwab, LIPID, Physiologie cellulaire et végétale (LPCV), Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Direction de Recherche Fondamentale (CEA) (DRF (CEA)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Université Grenoble Alpes (UGA), Light Photosynthesis & Metabolism (Photosynthesis), Modélisation et Exploration des Matériaux (MEM), Institut de Recherche Interdisciplinaire de Grenoble (IRIG), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Grenoble Alpes (UGA), Institut de biologie structurale (IBS - UMR 5075), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Integrated Structural Biology Grenoble (ISBG - UMS 3518 ), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-European Molecular Biology Laboratory [Grenoble] (EMBL)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), European Molecular Biology Laboratory (EMBL), Department of Biology [ETH Zürich] (D-BIOL), Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), This project received funding from the European Research Council: ERC Chloro-mito (grant no. 833184). Research was also supported by a Défi X-Life grant from CNRS, funds from the CEA DRF impulsion FIB-Bio program, the LabEx GRAL (ANR-10-LABX-49-01), financed within the University Grenoble Alpes graduate school (Ecoles Universitaires de Recherche) CBH-EUR-GS (ANR-17-EURE-0003) and the ANR ‘Momix’ (Projet-ANR-17-CE05-0029). This project also received funds from the European Union’s Horizon 2020 research and innovation programme CORBEL under the grant agreement No 654248. This work used the platforms of the Grenoble Instruct-ERIC centre (ISBG, UMS 3518 CNRS-CEA-UGA-EMBL) within the Grenoble Partnership for Structural Biology (PSB), supported by FRISBI (ANR-10-INBS-05-02) and GRAL. The electron microscope facility is supported by the Auvergne-Rhône-Alpes Region, the Fondation Recherche Medicale (FRM), the funds FEDER and the GIS-Infrastructures en Biologie Santé et Agronomie (IBISA). J.D. was supported by ATIP-Avenir program. C.U. is supported by a joint UGA-ETH Zurich PhD grant in the framework of the 'Investissements d’avenir' programme (ANR-15-IDEX-02). The authors thank the Roscoff Culture Collection that provided phytoplankton strains and Noan Le Bescot (Ternog Design) for help in the conception and realisation of the figures of this article., ANR-10-LABX-0049,GRAL,Grenoble Alliance for Integrated Structural Cell Biology(2010), ANR-17-CE05-0029,MoMix,Modélisation de la Mixotrophie chez l'algue extrêmophile Galdieria sulphuraria(2017), ANR-10-INBS-0005,FRISBI,Infrastructure Française pour la Biologie Structurale Intégrée(2010), ANR-15-IDEX-0002,UGA,IDEX UGA(2015), ANR-17-EURE-0003,CBH-EUR-GS,CBH-EUR-GS(2017), and Integrated Structural Biology Grenoble (ISBG)
Subjects: 0106 biological sciences, Abiotic component, 0303 health sciences, Biomass (ecology), Biotic component, Chemistry, [SDV]Life Sciences [q-bio], fungi, Genomics, 01 natural sciences, Chromatin, 03 medical and health sciences, Phytoplankton, Organelle, Biophysics, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, 030304 developmental biology, 010606 plant biology & botany, Biomineralization
Abstract: Phytoplankton is a minor fraction of the global biomass playing a major role in primary production and climate. Despite improved understanding of phytoplankton diversity and genomics, we lack nanoscale subcellular imaging approaches to understand their physiology and cell biology. Here, we present a complete Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM) workflow (from sample preparation to image processing) to generate nanometric 3D phytoplankton models. Tomograms of entire cells, representatives of six ecologically-successful phytoplankton unicellular eukaryotes, were used for quantitative morphometric analysis. Besides lineage-specific cellular architectures, we observed common features related to cellular energy management: i) conserved cell-volume fractions occupied by the different organelles; ii) consistent plastid-mitochondria interactions, iii) constant volumetric ratios in these energy-producing organelles. We revealed detailed subcellular features related to chromatin organization and to biomineralization. Overall, this approach opens new perspectives to study phytoplankton acclimation responses to abiotic and biotic factors at a relevant biological scale.
Published: 2020

45. On the Use of Rényi Entropy for Optimal Window Size Computation in the Short-Time Fourier Transform

Author: Marcelo A. Colominas, Sylvain Meignen, Duong-Hung Pham, Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET), CoMputational imagINg anD viSion (IRIT-MINDS), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, IEEE, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)
Subjects: Multicomponent signals, Relation (database), Computation, Short-time Fourier transform, Window (computing), 020206 networking & telecommunications, 02 engineering and technology, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Signal, Rényi entropy, 020303 mechanical engineering & transports, 0203 mechanical engineering, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, Modulation, 0202 electrical engineering, electronic engineering, information engineering, Short time Fourier transform, Algorithm, Mathematics
Abstract: International audience; In this paper, we investigate the determination of an optimal window length associated with the computation of the short time Fourier transform of multicomponent signals. In recent years the Rényi entropy has been widely used for that purpose, but the understanding of the significance of the obtained minimum in relation with the studied signal is still partial. In this paper, we explain in what way the window minimizing the Rényi entropy reflects the modulation of the modes making up the signal, and in which circumstances to use such a window is actually relevant.
Published: 2020
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46. Critical length and dimension elevation

Author: Beccari, Carolina, Casciola, Giulio, Mazure, Marie-Laurence, Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and UMR 5224
Subjects: critical length (for design), Extended Chebyshev spaces, geometric design, dimension elevation, [MATH]Mathematics [math], shape preservation
Published: 2020

47. Interpolation of G1 Hermite data by C1 cubic-like sparse Pythagorean hodograph splines

Author: Marie-Laurence Mazure, Rachid Ait-Haddou, Carolina Vittoria Beccari, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dipartimento di Matematica [Bologna], Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Ait-Haddou R., Beccari C.V., and Mazure M.-L.
Subjects: Monomial, Pure mathematics, Hermite polynomials, Pythagorean hodograph splines, Aerospace Engineering, 020207 software engineering, C1 interpolation, 02 engineering and technology, 01 natural sciences, Computer Graphics and Computer-Aided Design, Pythagorean hodograph, 0104 chemical sciences, Cubic-like sparse space, 010404 medicinal & biomolecular chemistry, Spline (mathematics), Planar, G1 Hermite data, Modeling and Simulation, Automotive Engineering, 0202 electrical engineering, electronic engineering, information engineering, Cubic-like sparse spaces, [MATH]Mathematics [math], Interpolation, Mathematics
Abstract: Provided that they are in appropriate configurations (tight data), given planar G 1 Hermite data generate a unique cubic Pythagorean hodograph (PH) spline curve interpolant. On a given associated knot-vector, the corresponding spline function cannot be C 1 , save for exceptional cases. By contrast, we show that replacing cubic spaces by cubic-like sparse spaces makes it possible to produce infinitely many C 1 PH spline functions interpolating any given tight G 1 Hermite data. Such cubic-like sparse spaces involve the constants and monomials of consecutive degrees, and they have long been used for design purposes. Only lately they were investigated in view of producing PH curves and associated G 1 PH spline interpolants with some flexibility. The present work strongly relies on these recent results.
Published: 2020
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48. No-slip and Free-slip divergence-free wavelets in three and higher dimension for the simulation of incompressible viscous flows

Author: Kadri, Souleymane, Perrier, Valérie, Université de La Rochelle (ULR), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), and Université Grenoble Alpes (UGA)
Subjects: Physics::Fluid Dynamics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: This work concerns divergence-free wavelet based methods for the numerical resolution of Navier-Stokes equations. It generalizes to higher dimension the approach of [23] that reformulates the projection method using the Helmholtz-Hodge decomposition in wavelet domain. The solution is searched in a finite dimensional free-slip divergence-free wavelet space, with time-dependent wavelet coefficients. We prove and verify the convergence of a first-order time numerical scheme for the Helmholtz-Hodge based projection method. Numerical simulations on the 3D Lid driven cavity flow show the accuracy and efficiency of the method.
Published: 2020

49. Fully Adaptive Ridge Detection Based on STFT Phase Information

Author: Sylvain Meignen, Duong-Hung Pham, Marcelo A. Colominas, Consejo Nacional de Investigaciones Científicas y Técnicas [Buenos Aires] (CONICET), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), CoMputational imagINg anD viSion (IRIT-MINDS), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées
Subjects: Otras Ingenierías y Tecnologías, Computer science, FREQUENCY MODULATION, BANDWIDTH, 02 engineering and technology, INGENIERÍAS Y TECNOLOGÍAS, time-frequency, [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], Instantaneous phase, symbols.namesake, [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, synchrosqueezing, TIME-FREQUENCY ANALYSIS, Applied Mathematics, Short-time Fourier transform, instantaneous frequency, 020206 networking & telecommunications, Time–frequency analysis, Fourier transform, Ridge detection, ridge detection, ESTIMATION, Signal Processing, short-time Fourier transform, symbols, Algorithm
Abstract: This letter deals with the problem of the estimation of the instantaneous frequencies of the modes of multicomponent signals from their linear time-frequency representations. In most approaches, such an estimation consists of extracting the ridges associated with each mode in the time-frequency plane. A major issue associated with these techniques is that ridge detection relies on some ad-hoc parameters which essentially bound the modulation of the studied modes and put some constraints on the type of filter used in the time-frequency representation. In this paper, we alternatively propose a novel fully adaptive approach for ridge detection whose relevance is shown throughout numerical simulations. Fil: Colominas, Marcelo Alejandro. Universidad Nacional de Entre Ríos. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática - Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática; Argentina Fil: Kuppel, Sylvain. Laboratoire Jean Kutzman, Universite de Grenoble; Francia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina Fil: Pham, Duong-Hung. Irit Laboratory, Cnrs Umr 5505, Toulouse, France; Francia
Published: 2020
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50. Lipschitz continuity of the eigenfunctions on optimal sets for functionals with variable coefficients

Author: Baptiste Trey, Institut Fourier (IF), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Calcul des Variations, Géométrie, Image (CVGI), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Trey, Baptiste, Laboratoire de Géologie de Lyon - Terre, Planètes, Environnement [Lyon] (LGL-TPE), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Géologie de Lyon - Terre, Planètes, Environnement (LGL-TPE), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut national des sciences de l'Univers (INSU - CNRS)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), and ANR-18-CE40-0013,SHAPO,Optimisation de forme(2018)
Subjects: Control and Optimization, Spectral optimization problem, the two-phase problem, Open set, Hölder condition, [MATH] Mathematics [math], 01 natural sciences, Combinatorics, symbols.namesake, Mathematics - Analysis of PDEs, 0103 physical sciences, FOS: Mathematics, Free boundary problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, [MATH]Mathematics [math], Eigenvalues and eigenvectors, Mathematics, 010102 general mathematics, Mathematics::Spectral Theory, Eigenfunction, Lipschitz continuity, free boundary problem, Computational Mathematics, almost-minimizer, Control and Systems Engineering, Dirichlet boundary condition, Bounded function, symbols, 010307 mathematical physics, Analysis of PDEs (math.AP)
Abstract: This paper is dedicated to the spectral optimization problemmin{λ1(Ω)+⋯+λk(Ω)+Λ|Ω| : Ω⊂Dquasi-open}whereD⊂ ℝdis a bounded open set and 0 <λ1(Ω) ≤⋯ ≤λk(Ω) are the firstkeigenvalues onΩof an operator in divergence form with Dirichlet boundary condition and Hölder continuous coefficients. We prove that the firstkeigenfunctions on an optimal set for this problem are locally Lipschtiz continuous inDand, as a consequence, that the optimal sets are open sets. We also prove the Lipschitz continuity of vector-valued functions that are almost-minimizers of a two-phase functional with variable coefficients.
Published: 2020
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