Publication Year Range: Last 50 years / Topic: 0101 mathematics - Searchworks@Jio Institute Digital Library Search Results

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1. A generic exact solver for vehicle routing and related problems

Author: Eduardo Uchoa, Artur Alves Pessoa, Ruslan Sadykov, François Vanderbeck, Universidade Federal Fluminense [Rio de Janeiro] (UFF), Reformulations based algorithms for Combinatorial Optimization (Realopt), Laboratoire Bordelais de Recherche en Informatique (LaBRI), 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)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Atoptima, We would like to thank Teobaldo Bulhoes and Guillaume Marques for a large part of the implementation of the Julia–JuMP interface to the solver, Teobaldo Bulhoes, Guillaume Marques and Eduardo Queiroga for implementing, over that interface, the models corresponding to the examples of this paper, and Laurent Facq for a general support of the computing environment. Experiments presented in this paper were carried out using the PlaFRIM (Federative Platform for Research in Computer Science and Mathematics), created under the Inria PlaFRIM development action with support from Bordeaux INP, LABRI and IMB and other entities: Conseil Régional d’Aquitaine, Université de Bordeaux, CNRS and ANR in accordance to the 'Programme d’Investissements d’Avenir'. This study was financed in part by the Conselho Nacional de Científico e Tecnológico (CNPq), grant 313601/2018-6 (Produtividade 1B), and by the Funda¸c˜ao de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ), grant E-26/202.887/2017 (Cientista do Estado)., Plafrim, 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)-Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Mathematical optimization, 021103 operations research, Bin packing problem, General Mathematics, Column generation, 0211 other engineering and technologies, Integer programming, Rule-based system, [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO], 010103 numerical & computational mathematics, 02 engineering and technology, Solver, 01 natural sciences, Vehicle routing problem, Path (graph theory), 0101 mathematics, Routing (electronic design automation), Software, Routing, Mathematics
Abstract: Major advances were recently obtained in the exact solution of vehicle routing problems (VRPs). Sophisticated branch-cut-and-price (BCP) algorithms for some of the most classical VRP variants now solve many instances with up to a few hundreds of customers. However, adapting and reimplementing those successful algorithms for other variants can be a very demanding task. This work proposes a BCP solver for a generic model that encompasses a wide class of VRPs. It incorporates the key elements found in the best existing VRP algorithms: ng-path relaxation, rank-1 cuts with limited memory, path enumeration, and rounded capacity cuts; all generalized through the new concepts of “packing set” and “elementarity set”. The concepts are also used to derive a branching rule based on accumulated resource consumption and to generalize the Ryan and Foster branching rule. Extensive experiments on several variants show that the generic solver has an excellent overall performance, in many problems being better than the best specific algorithms. Even some non-VRPs, like bin packing, vector packing and generalized assignment, can be modeled and effectively solved.
Published: 2020

2. Enclosings of decompositions of complete multigraphs in 2-edge-connected r -factorizations

Author: John Asplund, Pierre Charbit, Carl Feghali, Dalton State College, University System of Georgia (USG), Institut de Recherche en Informatique Fondamentale (IRIF (UMR_8243)), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Networks, Graphs and Algorithms (GANG), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-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), University of Bergen (UIB), This paper received partial support his paper received partial support by Fondation Sciences Mathématiques de Paris and the Research Council of Norway via the project CLASSIS, Grant Number 249994., and University of Bergen (UiB)
Subjects: Discrete mathematics, 010102 general mathematics, Multigraph, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], 0102 computer and information sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, Theoretical Computer Science, Combinatorics, Factorization, 010201 computation theory & mathematics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Discrete Mathematics and Combinatorics, Partition (number theory), Mathematics - Combinatorics, Combinatorics (math.CO), 0101 mathematics, ComputingMilieux_MISCELLANEOUS, Mathematics, 05B99
Abstract: A decomposition of a multigraph $G$ is a partition of its edges into subgraphs $G(1), \ldots , G(k)$. It is called an $r$-factorization if every $G(i)$ is $r$-regular and spanning. If $G$ is a subgraph of $H$, a decomposition of $G$ is said to be enclosed in a decomposition of $H$ if, for every $1 \leq i \leq k$, $G(i)$ is a subgraph of $H(i)$. Feghali and Johnson gave necessary and sufficient conditions for a given decomposition of $\lambda K_n$ to be enclosed in some $2$-edge-connected $r$-factorization of $\mu K_{m}$ for some range of values for the parameters $n$, $m$, $\lambda$, $\mu$, $r$: $r=2$, $\mu>\lambda$ and either $m \geq 2n-1$, or $m=2n-2$ and $\mu = 2$ and $\lambda=1$, or $n=3$ and $m=4$. We generalize their result to every $r \geq 2$ and $m \geq 2n - 2$. We also give some sufficient conditions for enclosing a given decomposition of $\lambda K_n$ in some $2$-edge-connected $r$-factorization of $\mu K_{m}$ for every $r \geq 3$ and $m = (2 - C)n$, where $C$ is a constant that depends only on $r$, $\lambda$ and~$\mu$., Comment: 17 pages; fixed the proof of Theorem 1.4 and other minor changes
Published: 2019

3. Towards a symplectic version of the Chevalley restriction theorem

Author: Ronan Terpereau, Manfred Lehn, Christian Lehn, Michael Bulois, Algèbre, géométrie, logique ( AGL ), Institut Camille Jordan [Villeurbanne] ( ICJ ), École Centrale de Lyon ( ECL ), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 ( UCBL ), Université de Lyon-Institut National des Sciences Appliquées de Lyon ( INSA Lyon ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ) -École Centrale de Lyon ( ECL ), Université de Lyon-Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Jean Monnet [Saint-Étienne] ( UJM ) -Centre National de la Recherche Scientifique ( CNRS ), Fakultät für Mathematik der Technischen Universität Chemnitz, Fakultaet fuer Mathematik der Technischen Universitaet Chemnitz, Institut für Mathematik ( MI ), Johannes Gutenberg - Universität Mainz ( JGU ), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Max Planck Institute for Mathematics ( Bonn ), The second-named author gratefully acknowledges the support by the DFG through the research grant Le 3093/2-1. The thirdnamed author is supported by the SFB Transregio 45 'Periods, Moduli Spaces and Arithmetic of Algebraic Varieties'. The fourth-named author is grateful to the Max-Planck-Institut für Mathematik of Bonn for the warm hospitality and support provided during the writing of this paper. Part ofthe genesis of this paper occurred during the half semester Algebraic Groups and Representations supported by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program 'Investissements d'Avenir' (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR)., ANR-11-IDEX-0007-02/10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon ( 2011 ), ANR-15-CE40-0012,GeoLie,GeoLie, Algèbre, géométrie, logique (AGL), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Chemnitz University of Technology / Technische Universität Chemnitz, Institut für Mathematik (MI), Johannes Gutenberg - Universität Mainz (JGU), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Max Planck Institute for Mathematics (MPIM), Max-Planck-Gesellschaft, ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010), and ANR-15-CE40-0012,GéoLie,Méthodes géométriques en théorie de Lie(2015)
Subjects: Polar representation, Symplectic variety, [ MATH.MATH-SG ] Mathematics [math]/Symplectic Geometry [math.SG], 01 natural sciences, Combinatorics, Mathematics - Algebraic Geometry, symbols.namesake, Morphism, 0103 physical sciences, FOS: Mathematics, 14L30, 53D20, 20G05, 20G20, 13A50, Representation Theory (math.RT), 0101 mathematics, MSC: 14L30, 53D20, 20G05, 20G20, 13A50, Mathematics::Representation Theory, Symplectic reduction, Algebraic Geometry (math.AG), Moment map, Mathematics, Weyl group, Algebra and Number Theory, Conjecture, [MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT], Reductive group, 010102 general mathematics, [MATH.MATH-SG]Mathematics [math]/Symplectic Geometry [math.SG], [ MATH.MATH-RT ] Mathematics [math]/Representation Theory [math.RT], [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG], Mathematics - Symplectic Geometry, symbols, Symplectic Geometry (math.SG), 010307 mathematical physics, Isomorphism, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], Mathematics - Representation Theory, Symplectic geometry
Abstract: If $(G,V)$ is a polar representation with Cartan subspace $\mathfrak c$ and Weyl group $W$, it is shown that there is a natural morphism of Poisson schemes $\mathfrak c \oplus {\mathfrak c}^*/W \to V\oplus V^*/\!\!/\!\!/ G$. This morphism is conjectured to be an isomorphism of the underlying reduced varieties if $(G,V)$ is visible. The conjecture is proved for visible stable locally free polar representations and certain further examples., Comment: 18 pages, final version
Published: 2017

4. Stability of optimal traffic plans in the irrigation problem

Author: Antoine Prouff, Antonio De Rosa, Andrea Marchese, Maria Colombo, Paul Pegon, Ecole Polytechnique Fédérale de Lausanne (EPFL), Courant Institute of Mathematical Sciences [New York] (CIMS), New York University [New York] (NYU), NYU System (NYU)-NYU System (NYU), Department of mathematics/Dipartimento di Matematica [Univ. Trento], Università degli Studi di Trento (UNITN), 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), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), 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)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), Maria Colombo was partially supported by the Swiss National Science Foundation grant 200021_182565. Antonio De Rosa has been supported by the NSF DMS Grant No. 1906451. Andrea Marchese acknowledges partial support from GNAMPA-INdAM., Department of Mathematics [College Park], University of Maryland [College Park], University of Maryland System-University of Maryland System, Bocconi Institute for Data Science and Analytics (BIDSA), Bocconi University [Milan, Italy], 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 sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, M. C. was partially supported by the Swiss National Science Foundation grant 200021_182565. A. D. R. has been supported by the NSF DMS Grant No. 1906451 and the NSF DMS Grant No. 2112311. A. M. acknowledges partial support from GNAMPA-INdAM. A.P. was supported by the Fondation Mathématiques Jacques Hadamard. P.P and A.P. both acknowledge EPFL for hosting them during the semester this paper was prepared., Inria de Paris, and 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)
Subjects: BRANCHED TRANSPORT, Mathematical optimization, Irrigation, TRAFFIC PLANS, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, Stability (probability), symbols.namesake, Mathematics - Analysis of PDEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Computer Science::Networking and Internet Architecture, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Discrete Mathematics and Combinatorics, Limit (mathematics), 0101 mathematics, Mathematics - Optimization and Control, Mathematics, TRANSPORTATION NETWORK, BRANCHED TRANSPORT, IRRIGATION PROBLEM, TRAFFIC PLANS, STABILITY, STABILITY, IRRIGATION PROBLEM, Applied Mathematics, TRANSPORTATION NETWORK, 010102 general mathematics, Eulerian path, Flow network, 010101 applied mathematics, Optimization and Control (math.OC), Mathematics - Classical Analysis and ODEs, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Analysis, Lagrangian, Analysis of PDEs (math.AP)
Abstract: We prove the stability of optimal traffic plans in branched transport. In particular, we show that any limit of optimal traffic plans is optimal as well. This result goes beyond the Eulerian stability proved in [7], extending it to the Lagrangian framework.
Published: 2022

5. A general global-local modelling framework for the deterministic optimisation of composite structures

Author: Marco Picchi Scardaoni, Marco Montemurro, Institut de Mécanique et d'Ingénierie de Bordeaux (I2M), École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Institut National de la Recherche Agronomique (INRA), University of Pisa - Università di Pisa, and This paper presents part of the activities carried out within the research project PARSIFAL ('PrandtlPlane ARchitecture for the Sustainable Improvement of Future AirpLanes'), which has been funded by the European Union under the Horizon 2020 Research and Innovation Program (Grant Agreement n.723149)
Subjects: Mathematical optimization, Control and Optimization, Cantilever, Local modelling approach, Computer science, 0211 other engineering and technologies, 02 engineering and technology, Marsaglia polar method, Design strategy, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], 01 natural sciences, Polar method, 021105 building & construction, Mécanique: Mécanique des structures [Sciences de l'ingénieur], 0101 mathematics, Anisotropy, Composites, Buckling, Deterministic optimisation, Global/local modelling approach, Deterministic Optimisation, Mécanique: Mécanique des solides [Sciences de l'ingénieur], Global, Optimisation et contrôle [Mathématique], Computer Graphics and Computer-Aided Design, Computer Science Applications, Design for manufacturability, 010101 applied mathematics, [SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph], Control and Systems Engineering, Macroscopic scale, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Engineering design process, Software
Abstract: International audience; This work deals with the multi-scale optimisation of composite structures by adopting a general global-local (GL) modelling strategy to assess the structure responses at different scales. The GL modelling approach is integrated into the multi-scale two-level optimisation strategy (MS2LOS) for composite structures. The resulting design strategy is, thus, called GL-MS2LOS and aims at proposing a very general formulation of the design problem, without introducing simplifying hypotheses on the laminate stack and by considering, as design variables, the full set of geometric and mechanical parameters defining the behaviour of the composite structure at each pertinent scale. By employing a GL modelling approach, most of the limitations of well-established design strategies, based on analytical or semi-empirical models, are overcome. The GL-MS2LOS makes use of the polar formalism to describe the anisotropy of the composite at the macroscopic scale (where it is modelled as an equivalent homogeneous anisotropic plate). In this work, deterministic algorithms are exploited during the solution search phase. The challenge, when dealing with such a design problem, is to develop a suitable formulation and dedicated operators, to link global and local models physical responses and their gradients. Closed-form expressions of structural responses gradients are rigorously derived by taking into account for the coupling effects when passing from global to local models. The effectiveness of the GL-MS2LOS is proven on a meaningful benchmark: the least-weight design of a cantilever wing subject to different design requirements. Constraints include maximum allowable displacements, maximum allowable strains, blending, manufacturability requirements and buckling factor.; This work deals with the multi-scale optimisation of composite structures by adopting a general global-local (GL) modelling strategy to assess the structure responses at different scales. The GL modelling approach is integrated into the multi-scale two-level optimisation strategy (MS2LOS) for composite structures. The resulting design strategy is, thus, called GL-MS2LOS and aims at proposing a very general formulation of the design problem, without introducing simplifying hypotheses on the laminate stack and by considering, as design variables, the full set of geometric and mechanical parameters defining the behaviour of the composite structure at each pertinent scale. By employing a GL modelling approach, most of the limitations of well-established design strategies, based on analytical or semi-empirical models, are overcome. The GL-MS2LOS makes use of the polar formalism to describe the anisotropy of the composite at the macroscopic scale (where it is modelled as an equivalent homogeneous anisotropic plate). In this work, deterministic algorithms are exploited during the solution search phase. The challenge, when dealing with such a design problem, is to develop a suitable formulation and dedicated operators, to link global and local models physical responses and their gradients. Closed-form expressions of structural responses gradients are rigorously derived by taking into account for the coupling effects when passing from global to local models. The effectiveness of the GL-MS2LOS is proven on a meaningful benchmark: the least-weight design of a cantilever wing subject to different design requirements. Constraints include maximum allowable displacements, maximum allowable strains, blending, manufacturability requirements and buckling factor.
Published: 2020

6. Mixture modeling for identifying subtypes in disease course mapping

Author: Stanley Durrleman, Pierre-Emmanuel Poulet, Algorithms, models and methods for images and signals of the human brain (ARAMIS), Sorbonne Université (SU)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute (ICM), Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), This research has received funding from the program 'Investissements d’avenir' ANR-10-IAIHU-06. This work was also funded in part by the French government under management of Agence Nationale de la Recherche as part of the 'Investissements d’avenir' program, reference ANR-19-P3IA-0001 (PRAIRIE 3IA Institute)., Aasa Feragen, Stefan Sommer, Julia Schnabel, Mads Nielsen, ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut du Cerveau et de la Moëlle Epinière = Brain and Spine Institute (ICM), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut du Cerveau = Paris Brain Institute (ICM), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Institut du Cerveau = Paris Brain Institute (ICM), Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Sorbonne Université (SU)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), This paper is funded in part by grant number 678304 (ERC), 826421 (TVB-Cloud) from H2020 programme, and ANR-10-IAIHU-06 (IHU ICM), ANR-19-P3IA-0001 (PRAIRIE) and ANR-19-JPW2-000 (E-DADS) from ANR., Poulet, Pierre-Emmanuel, PaRis Artificial Intelligence Research InstitutE - - PRAIRIE2019 - ANR-19-P3IA-0001 - P3IA - VALID, Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-CHU Pitié-Salpêtrière [AP-HP], Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Assistance publique - Hôpitaux de Paris (AP-HP) (AP-HP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Computer science, Population, Stochastic approximation, Machine learning, computer.software_genre, 01 natural sciences, Synthetic data, 010104 statistics & probability, 03 medical and health sciences, 0302 clinical medicine, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Alzheimer's disease subtypes, mixed-effect models, 0101 mathematics, Cognitive decline, mixture models, education, Cluster analysis, Non-linear mixed-effect model, ComputingMilieux_MISCELLANEOUS, Mixture model, Ground truth, education.field_of_study, MCMC-SAEM, business.industry, Contrast (statistics), Disease course mapping, Disease progression modelling, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Artificial intelligence, business, computer, [STAT.ME]Statistics [stat]/Methodology [stat.ME], 030217 neurology & neurosurgery
Abstract: International audience; Disease modeling techniques summarize the possible trajectories of progression from multimodal and longitudinal data. These techniques often assume that individuals form a homogeneous cluster, thus ignoring possible disease subtypes within the population. We extend a non-linear mixed-effect model used for disease course mapping with a mixture framework. We jointly estimate model parameters and subtypes with a tempered version of a stochastic approximation of the Expectation Maximisation algorithm. We show that our model recovers the ground truth parameters from synthetic data, in contrast to the naive solution consisting in post hoc clustering of individual parameters from a one-class model. Applications to Alzheimer's disease data allows the unsupervised identification of disease subtypes associated with distinct relationship between cognitive decline and progression of imaging and biological biomarkers.
Published: 2021

7. Modeling Interactions among Migration, Growth and Pressure in Tumor Dynamics

Author: Juan Campos, Juan José Soler, Juan Melchor, Beatriz Blanco, [Blanco, Beatriz] Univ Granada, Dept Struct Mech, Granada 18071, Spain, [Blanco, Beatriz] Ibs GRANADA, Inst Invest Biosanitaria, Granada 18012, Spain, [Melchor, Juan] Ibs GRANADA, Inst Invest Biosanitaria, Granada 18012, Spain, [Campos, Juan] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada 18071, Spain, [Soler, Juan] Univ Granada, Fac Ciencias, Dept Matemat Aplicada, Granada 18071, Spain, [Campos, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Melchor, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Soler, Juan] Univ Granada, Res Unit Modelling Nat MNat, Granada 18071, Spain, [Melchor, Juan] Univ Granada, Dept Stat & Operat Res, Granada 18071, Spain, MINECO-Feder (Spain), Junta de Andalucia (Spain), Instituto de Salud Carlos III, Ministry of Science, Innovation and Universities of Spain, Consejeria de Economia, Conocimiento, Empresas y Universidad, European Regional Development Fund (ERDF), [Blanco,B] Department of Structural Mechanics, University of Granada, Granada, Spain. [Blanco,B, Melchor,J] Instituto de Investigación Biosanitaria, ibs.GRANADA, Granada, Spain. [Campos,J, Soler,J] Departamento de Matemática Aplicada, Facultad de Ciencias, Universidad de Granada, Granada, Spain. [Campos,J, Melchor,J, Soler,J] Research Unit 'Modelling Nature' (MNat), Universidad de Granada, Granada, Spain., and This paper has been partially supported by the MINECO-Feder (Spain) research grant num bers RTI2018-098850-B-I00 (J.C., J.S.) & EQC2018-004508-P (B.B., J.M.), the Junta de Andalucía (Spain) Projects PY18-RT-2422 (J.C., J.S.), A-FQM-311-UGR18 (J.C., J.S.) & IE2017-5537 (B.B., J.M.), and by the Instituto de Salud Carlos III, project number DTS17/00087 (J.M., J.S.). This study was also funded by Ministry of Science, Innovation and Universities of Spain, project numbers DPI2017-85359-R (B.B., J.M.) & PID2019-106947RA-C22 (B.B., J.M.) and by Consejería de Economía, Conocimiento, Empresas y Universidad and European Regional Development Fund (ERDF), ref. SOMM17/6109/UGR (J.C., J.M., J.S.). Lastly, B.B. research was granted by Ministry of Science, Innovation and Universities of Spain, FPU2017/01415.
Subjects: Computer science, 01 natural sciences, Forces, Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Movement [Medical Subject Headings], Diffusion, porous media, Qualitative behavior, Computer Science (miscellaneous), Numerical simulations, Homeostasis, Statistical physics, Diffusion (business), Solid tumor, Analytical, Diagnostic and Therapeutic Techniques and Equipment::Investigative Techniques::Epidemiologic Methods::Data Collection::Vital Statistics::Mortality::Cause of Death [Medical Subject Headings], Cancer, 0303 health sciences, Partial differential equation, Mathematical modelling, Dynamics (mechanics), Traveling-waves, mathematical modeling, tumor dynamics, Phenomena and Processes::Chemical Phenomena::Biochemical Phenomena::Biochemical Processes::Signal Transduction [Medical Subject Headings], Diseases::Neoplasms [Medical Subject Headings], flux-saturated, Modelos teóricos, General Mathematics, Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::Porosity [Medical Subject Headings], Context (language use), Information Science::Information Science::Communication::Cybernetics::Feedback [Medical Subject Headings], cell motility, Stress, Mechanics, 03 medical and health sciences, QA1-939, Hele-Shaw model, Movimiento celular, Phenomena and Processes::Physical Phenomena::Mechanical Phenomena::Elasticity [Medical Subject Headings], 0101 mathematics, Engineering (miscellaneous), 030304 developmental biology, Computer simulation, 010102 general mathematics, Porous-media equations, Mass, numerical simulation, Floculadores, Phenomena and Processes::Cell Physiological Phenomena::Cell Physiological Processes::Cell Transdifferentiation::Epithelial-Mesenchymal Transition [Medical Subject Headings], mechanical feedback, Phenomena and Processes::Physiological Phenomena::Physiological Processes::Homeostasis [Medical Subject Headings], Mathematics
Abstract: What are the biomechanical implications in the dynamics and evolution of a growing solid tumor? Although the analysis of some of the biochemical aspects related to the signaling pathways involved in the spread of tumors has advanced notably in recent times, their feedback with the mechanical aspects is a crucial challenge for a global understanding of the problem. The aim of this paper is to try to illustrate the role and the interaction between some evolutionary processes (growth, pressure, homeostasis, elasticity, or dispersion by flux-saturated and porous media) that lead to collective cell dynamics and defines a propagation front that is in agreement with the experimental data. The treatment of these topics is approached mainly from the point of view of the modeling and the numerical approach of the resulting system of partial differential equations, which can be placed in the context of the Hele-Shaw-type models. This study proves that local growth terms related to homeostatic pressure give rise to retrograde diffusion phenomena, which compete against migration through flux-saturated dispersion terms., MINECO-Feder (Spain) research grant numbers RTI2018-098850-B-I00 (J.C., J.S.) & EQC2018-004508-P (B.B., J.M.), Junta de Andalucía (Spain) Projects PY18-RT-2422 (J.C., J.S.), A-FQM-311-UGR18 (J.C., J.S.) & IE2017-5537 (B.B., J.M.), Instituto de Salud Carlos III, project number DTS17/00087 (J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, project numbers DPI2017-85359-R (B.B., J.M.) & PID2019-106947RA-C22 (B.B., J.M.), Consejería de Economía, Conocimiento, Empresas y Universidad and European Regional Development Fund (ERDF), ref. SOMM17/6109/UGR (J.C., J.M., J.S.), Ministry of Science, Innovation and Universities of Spain, FPU2017/01415
Published: 2021

8. Some analytical solutions for validation of free surface flow computational codes

Author: Bernard Di Martino, Fabien Souillé, Jacques Sainte-Marie, Marie-Odile Bristeau, Anne Mangeney, Numerical Analysis, Geophysics and Ecology (ANGE), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Institut de Physique du Globe de Paris (IPGP (UMR_7154)), Institut national des sciences de l'Univers (INSU - CNRS)-Université de La Réunion (UR)-Institut de Physique du Globe de Paris (IPG Paris)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), The work presented in this paper was supported in part by the ANR Mimosa (ANR-14-CE01-0012) and ERC contract ERC-CG-2013-PE10-617472 SLIDEQUAKES. The authors also acknowledge the Inria Project Lab 'Algae in Silico' for its financial support., ANR-14-CE01-0012,MIMOSA,Analyse, modélisation et utilisation du bruit sismique large bande: des microséismes aux oscillations libres de la terre(2014), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Institut de Physique du Globe de Paris (IPGP), Institut national des sciences de l'Univers (INSU - CNRS)-IPG PARIS-Université de La Réunion (UR)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université de La Réunion (UR)-Université Paris Diderot - Paris 7 (UPD7)-IPG PARIS-Institut national des sciences de l'Univers (INSU - CNRS)
Subjects: 010103 numerical & computational mathematics, Analytical solutions, 01 natural sciences, law.invention, Physics::Fluid Dynamics, Free surface Euler equations, symbols.namesake, law, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, [MATH]Mathematics [math], Mathematics, Computer simulation, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Mechanics of the fluids [physics.class-ph], Mechanical Engineering, Mechanics, Euler system, Condensed Matter Physics, River dynamics, Euler equations, 010101 applied mathematics, Flow (mathematics), Mechanics of Materials, Free surface, symbols, Compressibility, Hydrostatic equilibrium
Abstract: We present several time dependent analytical solutions for the incompressible Euler system with free surface. These analytical solutions give quantitative descriptions of some physical phenomena and can be used as reference solutions when validating numerical simulation codes. They concern fluid flows governed by Euler equations with or withouthydrostatic hypothesis including wet/dry interface, variable density, wide variety of boundary conditions and possibly non-uniform bottom topographies. Some of these analytical solutions concern shallow water type models or free surface Navier-Stokes model i.e. with a viscous fluid.
Published: 2021

9. The DGDD Method for Reduced-Order Modeling of Conservation Laws

Author: Angelo Iollo, Charbel Farhat, Sebastian Grimberg, Michel Bergmann, Sébastien Riffaud, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Modeling Enablers for Multi-PHysics and InteractionS (MEMPHIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Aeronautics and Astronautics [Stanford] (AA Stanford), Stanford University, Department of Mechanical Engineering [Stanford], Institute for Computational and Mathematical Engineering [Stanford] (ICME), This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement N° 872442. Experiments presented in this paper were carried out using the PlaFRIM experimental testbed, supported by Inria, CNRS (LABRI and IMB), Université de Bordeaux, Bordeaux INP and Conseil Régional d’Aquitaine (see https://www.plafrim.fr/)., Plafrim, MEMPHIS, European Project: 872442,ARIA, European Project: 872442,ARIA(2019), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest
Subjects: ECSW method, Polynomial, Physics and Astronomy (miscellaneous), Proper Orthogonal Decomposition, 010103 numerical & computational mathematics, 01 natural sciences, symbols.namesake, Discontinuous Galerkin method, Applied mathematics, Domain decomposition, 0101 mathematics, Representation (mathematics), Parametric statistics, Mathematics, Numerical Analysis, Conservation law, Applied Mathematics, Domain decomposition methods, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, Computer Science Applications, Euler equations, 010101 applied mathematics, Reduced-order model, Computational Mathematics, Modeling and Simulation, symbols, Reduction (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: International audience; The discontinuous Galerkin domain decomposition (DGDD) method couples subdomains of high-fidelity polynomial approximation to regions of low-dimensional resolution for the numerical solution of systems of conservation laws. In the low-fidelity regions, the solution is approximated by empirical modes constructed by Proper Orthogonal Decomposition and a reduced-order model is used to predict the solution. The high-dimensional model instead solves the system of conservation laws only in regions where the solution is not amenable to a low-dimensional representation. The coupling between the high-dimensional and the reduced-order models is then performed in a straightforward manner through numerical fluxes at discrete cell boundaries. We show results from application of the proposed method to parametric problems governed by the quasi-1D and 2D compressible Euler equations. In particular, we investigate the prediction of unsteady flows in a converging-diverging nozzle and over a NACA0012 airfoil in presence of shocks. The results demonstrate the stability and the accuracy of the proposed method and the significant reduction of the computational cost with respect to the high-dimensional model.
Published: 2021

10. Diffusion-redistanciation schemes for 2D and 3D constrained Willmore flow: application to the equilibrium shapes of vesicles

Author: Emmanuel Maitre, Mourad E. H. Ismail, Arnaud Sengers, Thibaut Metivet, ModELisation de l'apparence des phénomènes Non-linéaires (ELAN), 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), Equations aux Dérivées Partielles (EDP), 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 ), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] (DYFCOM-LIPhy ), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Most of the computations presented in this paper were performed using the Froggy platform of the GRICAD infrastructure (https://gricad.univ-grenoble-alpes.fr), which is supported by the Rhône-Alpes region (GRANT CPER07_13 CIRA) and the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche, and the Atlas cluster from the Research Institute in Advanced Mathematics (IRMA - UMR7501)., ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), 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-....])-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-....]), 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-....]), DYnamique des Fluides COmplexes et Morphogénèse [Grenoble] [2020-….] (DYFCOM-LIPhy [2020-….]), Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] [2020-….] (LIPhy [2020-….]), and Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Centre National de la Recherche Scientifique (CNRS)
Subjects: Volume and area preserving, Vol- ume and area preserving, Diffusion generated motion, Physics and Astronomy (miscellaneous), Computer science, Interface (Java), and phrases: Diffusion generated motion, Signed distance function, Clifford torus, 010103 numerical & computational mathematics, Willmore flow, 01 natural sciences, Level set, Dimension (vector space), FOS: Mathematics, Applied mathematics, Mathematics - Numerical Analysis, [PHYS.MECA.MEFL]Physics [physics]/Mechanics [physics]/Fluid mechanics [physics.class-ph], 0101 mathematics, Diffusion (business), [MATH]Mathematics [math], High-order geometrical flow, Numerical Analysis, Level set (data structures), Applied Mathematics, Numerical Analysis (math.NA), Thresholding, Computer Science Applications, 010101 applied mathematics, Computational Mathematics, Flow (mathematics), Modeling and Simulation, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract: In this paper we present a novel algorithm for simulating geometrical flows, and in particular the Willmore flow, with conservation of volume and area. The idea is to adapt the class of diffusion-redistanciation algorithms to the Willmore flow in both two and three dimensions. These algorithms rely on alternating diffusions of the signed distance function to the interface and a redistanciation step, and with careful choice of the applied diffusions, end up moving the zero level-set of the distance function by some geometrical quantity without resorting to any explicit transport equation. The constraints are enforced between the diffusion and redistanciation steps via a simple rescaling method. The energy globally decreases at the end of each global step. The algorithms feature the computational efficiency of thresholding methods without requiring any adaptive remeshing thanks to the use of a signed distance function to describe the interface. This opens their application to dynamic fluid-structure simulations for large and realistic cases. The methodology is validated by computing the equilibrium shapes of two- and three-dimensional vesicles, as well as the Clifford torus.
Published: 2020

11. The fast iterated bootstrap

Author: Mirza Trokic, Russell Davidson, McGill University = Université McGill [Montréal, Canada], Centre interuniversitaire de recherche en économie quantitative (CIREQ), Aix-Marseille Sciences Economiques (AMSE), École des hautes études en sciences sociales (EHESS)-Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), IHS Markit, and This research was supported by the Canada Research Chair program (Chair in Economics, McGill University), and by grants from the Social Sciences and Humanities Research Council of Canada and the Fonds de Recherche du QuebecSociete Culture, Canada. We are grateful to seminar participants at the Third French Econometric Conference, the Singapore Management University, the Hong Kong University of Science and Technology, and the University of Sydney, for useful comments. We also thank our discussant Matt Webb for insightful comments at the 2017 CESG. Our thanks go to three anonymous referees and a guest co-editor for insightful comments that helped us improve the paper.
Subjects: Economics and Econometrics, Series (mathematics), Computer science, Applied Mathematics, 05 social sciences, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C12 - Hypothesis Testing: General, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C10 - General, Sense (electronics), [SHS.ECO]Humanities and Social Sciences/Economics and Finance, 01 natural sciences, Power (physics), Bootstrap iteration Fast iterated bootstrap, 010104 statistics & probability, JEL: C - Mathematical and Quantitative Methods/C.C6 - Mathematical Methods • Programming Models • Mathematical and Simulation Modeling/C.C6.C63 - Computational Techniques • Simulation Modeling, Null (SQL), Iterated function, Distortion, 0502 economics and business, bootstrap iteration, fast iterated bootstrap, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C15 - Statistical Simulation Methods: General, 0101 mathematics, Algorithm, 050205 econometrics
Abstract: International audience; The standard forms of bootstrap iteration are very computationally demanding. As a result, there have been several attempts to alleviate the computational burden by use of approximations. In this paper, we extend the fast double bootstrap of Davidson and MacKinnon (2007) to higher orders of iteration, and provide algorithms for their implementation. The new methods make computational demands that increase only linearly with the level of iteration, unlike standard procedures, whose demands increase exponentially. In a series of simulation experiments, we show that the fast triple bootstrap improves on both the standard and fast double bootstraps, in the sense that it suffers from less size distortion under the null with no accompanying loss of power.
Published: 2020

12. Sub-quadratic time for Riemann-Roch spaces. The case of smooth divisors over nodal plane projective curves

Author: Alain Couvreur, Grégoire Lecerf, Simon Abelard, Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), Geometry, arithmetic, algorithms, codes and encryption (GRACE), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This paper is a part of a project that has received funding by the French Agence de l'Innovation de Défense (DGA)., Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Inria Saclay - Ile de France, Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), and Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
Subjects: Projective curve, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], [INFO.INFO-CC]Computer Science [cs]/Computational Complexity [cs.CC], Pure mathematics, Basis (linear algebra), Plane (geometry), 010102 general mathematics, MathematicsofComputing_NUMERICALANALYSIS, 010103 numerical & computational mathematics, Space (mathematics), 01 natural sciences, Riemann hypothesis, symbols.namesake, Mathematics::Algebraic Geometry, TheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITY, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, symbols, Algebraic curve, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, Projective test, Time complexity, Mathematics
Abstract: International audience; We revisit the seminal Brill-Noether algorithm in the rather generic situation of smooth divisors over a nodal plane projective curve. Our approach takes advantage of fast algorithms for polynomials and structured matrices. We reach sub-quadratic time for computing a basis of a Riemann-Roch space. This improves upon previously known complexity bounds.
Published: 2020

13. Online estimation of integrated squared density derivatives

Author: Abdelkader Mokkadem, Mariane Pelletier, Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and We deeply thank the Referees for their thoughtful remarks, which led to a substantially improved version of our paper.
Subjects: Statistics and Probability, Recursive estimation, Mean squared error, 010102 general mathematics, Bandwidth (signal processing), Estimator, Probability density function, Density estimation, Online estimation, Rate of convergence, Stochastic algorithm, 01 natural sciences, 010104 statistics & probability, Kernel estimators of integrals, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Applied mathematics, 0101 mathematics, Statistics, Probability and Uncertainty, Mathematics, Parametric statistics
Abstract: Hall and Marron (1987) introduced kernel estimators of integrals of the squared m -order derivatives of a probability density. Mokkadem and Pelletier (2020) gave recursive versions of their estimators, but the main drawback of these estimators is that their update requires the use of all past data. The aim of this paper is the study of online versions of the estimators introduced by Hall and Marron (1987), that is of estimators which are not only recursive, but which also have the property that their update uses only the last available data. Rates of convergence in mean squared error (MSE) are calculated. Similarly to the estimators of Hall and Marron (1987) and of Mokkadem and Pelletier (2020), our online estimators achieve the parametric rate n − 1 when m = 0 or when higher order kernels are used. For the case when the parametric rate is not obtained, we also study an online version of the estimator proposed by Jones and Sheather (1991). Finally, we provide recursive estimators of the optimal bandwidth in the framework of density estimation.
Published: 2020

14. Powers of conjugacy classes in a finite groups

Author: Carmen Melchor, Antonio Beltrán, Rachel Camina, María José Felipe, Apollo - University of Cambridge Repository, and Part of this paper was written during the stay of C. Melchor at the University of Cambridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castellón. C. Melchor would like to thank R. Camina and the Department of Mathematics for their warm hospitality. A. Beltrán, M.J. Felipe and C. Melchor are supported by Proyecto PGC2018-096872-B-100, Ministerio de Ciencia, Innovación y Universidades.
Subjects: Finite group, business.industry, Applied Mathematics, 010102 general mathematics, 4904 Pure Mathematics, Power of conjugacy classes, 01 natural sciences, Finite groups, Conjugacy classes, Mathematics::Group Theory, Conjugacy class, Hospitality, Solvability, 0103 physical sciences, 49 Mathematical Sciences, 010307 mathematical physics, Sociology, Characters, 0101 mathematics, business, MATEMATICA APLICADA, Humanities, Matemàtica
Abstract: [EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability concerning the case in which the power of a conjugacy class is a union of one or two conjugacy classes. Moreover, we show that the above conditions can be determined through the character table of the group., Part of this paper was written during the stay of C.Melchor at the University of Cambridge in autumn 2017, which was financially supported by the grant E-2017-02, Universitat Jaume I of Castellón. C. Melchor would like to thank R. Camina and the Department of Mathematics for their warm hospitality. A. Beltrán, M.J. Felipe and C. Melchor are supported by Proyecto PGC2018-096872-B-100, Ministerio de Ciencia, Innovación y Universidades.
Published: 2020

15. Informal caregiving and physical activity among 204,315 adults in 38 low- and middle-income countries: A cross-sectional study

Author: Louis Jacob, Brendon Stubbs, Ai Koyanagi, Lee Smith, Davy Vancampfort, Sarah E Jackson, Josep Maria Haro, Jae Il Shin, Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), ICA-CL-2017-03-001 Maudsley Charity Collaboration for Leadership in Applied Health Research and Care - Greater Manchester, CLAHRC GM National Institute for Health Research, NIHR King's College London Instituto de Salud Carlos III, ISCIII European Regional Development Fund, ERDF Collaboration for Leadership in Applied Health Research and Care - Greater Manchester, CLAHRC GM, and Ai Koyanagi's work is supported by the PI15/00862 project, integrated into the National R + D + I and funded by the ISCIII - General Branch Evaluation and Promotion of Health Research - and the European Regional Development Fund (ERDF-FEDER). Brendon Stubbs is supported by a Clinical Lectureship ( ICA-CL-2017-03-001 ) jointly funded by Health Education England (HEE) and the National Institute for Health Research (NIHR). Brendon Stubbs is part funded by the NIHR Biomedical Research Centre at South London and Maudsley NHS Foundation Trust . Brendon Stubbs is also supported by the Maudsley Charity , King's College London and the NIHR South London Collaboration for Leadership in Applied Health Research and Care - Greater Manchester (CLAHRC) funding. This paper presents independent research. The views expressed in this publication are those of the authors and not necessarily those of the acknowledged institutions.
Subjects: Male, STRESS, IMPACT, Cross-sectional study, Epidemiology, [SDV]Life Sciences [q-bio], Global Health, 01 natural sciences, 0302 clinical medicine, Prevalence, Medicine, 030212 general & internal medicine, Public, Environmental & Occupational Health, RISK, Low- and middle-income countries, HEALTH BEHAVIORS, OF-LIFE, ASSOCIATION, Multi-country study, FAMILY, PREVALENCE, 3. Good health, Caregivers, Informal caregiving, Female, Life Sciences & Biomedicine, MENTAL-HEALTH, Adult, medicine.medical_specialty, Physical activity, World health, 03 medical and health sciences, Medicine, General & Internal, General & Internal Medicine, Environmental health, Humans, 0101 mathematics, Developing Countries, Exercise, Poverty, Science & Technology, business.industry, DISABILITY, 010102 general mathematics, Public Health, Environmental and Occupational Health, Health Surveys, Cross-Sectional Studies, Low and middle income countries, business
Abstract: Data on the association between informal caregiving and physical activity (PA) levels are scarce, especially from low- and middle-income countries (LMICs). Furthermore, previous research has yielded conflicting results. Thus, we investigated this association in adults from 38 LMICs. Data from the World Health Survey (WHS), a cross-sectional, predominantly nationally representative survey conducted in 2002-2004, were analyzed. PA was assessed by the International Physical Activity Questionnaire and participants were dichotomized into those who do (≥150 min of moderate-to-vigorous PA per week) and do not (
Published: 2019

16. Combining Analytical Approaches and Multiple Sources of Information to Improve Interpretation of Diagnostic Test Results for Tuberculosis in Wild Meerkats

Author: Stuart J. Patterson, Charlene Clarke, Tim H. Clutton-Brock, Michele A. Miller, Sven D. C. Parsons, Dirk U. Pfeiffer, Timothée Vergne, Julian A. Drewe, Patterson, Stuart J [0000-0002-4907-8373], Clarke, Charlene [0000-0002-9497-2614], Miller, Michele A [0000-0002-5883-6076], Parsons, Sven DC [0000-0002-9033-9686], Pfeiffer, Dirk U [0000-0001-7000-0530], Drewe, Julian A [0000-0003-0709-8066], Apollo - University of Cambridge Repository, Veterinary Epidemiology, Economics and Public Health Group, Royal Veterinary College, SAMRC Centre for TB Research, Stellenbosch University, Mammal Research Institute, Department of Zoology and Entomology [Pretoria], University of Pretoria [South Africa]-University of Pretoria [South Africa], Large Animal Research Group, University of Cambridge [UK] (CAM), Department of Infectious Diseases and Public Health, City University of Hong Kong [Hong Kong] (CUHK), Interactions hôtes-agents pathogènes [Toulouse] (IHAP), Ecole Nationale Vétérinaire de Toulouse (ENVT), Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), This paper has relied on records of individual identities and life histories maintained by the Kalahari Meerkat Project, which is supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 294494), the Human Frontier Science Program (funding reference RGP0051/2017), the University of Zurich, the Swiss National Science Foundation and the Mammal Research Institute at the University of Pretoria, South Africa. This specific work was funded by BBSRC (training scholarship BB/F016891/1), the Royal Veterinary College and the Friends of the Kalahari Meerkat Project, kalahari-meerkats.com/fkmp. Thanks also to Irene Staehelin for her generous support. This research was funded partially by the South African government through the South African Medical Research Council and the National Research Foundation South African Research Chair Initiative (Grant #86949). MM, CC, and SP were supported by the South African government through the South African Medical Research Council and the National Research Foundation Chair Initiative (grant #86949)., and European Project: 294494,EC:FP7:ERC,ERC-2011-ADG_20110310,THCB2011(2012)
Subjects: General Veterinary, 040301 veterinary sciences, [SDV]Life Sciences [q-bio], wildlife, Veterinary medicine, diagnostics, interpretation, tuberculosis, meerkats, 04 agricultural and veterinary sciences, 01 natural sciences, Article, 3. Good health, 0403 veterinary science, 010104 statistics & probability, QL1-991, SF600-1100, Animal Science and Zoology, 0101 mathematics, Zoology
Abstract: Data presented in this study is publicly available at https://figshare.com/s/45bd5369a97b4c2489bf (accessed on 25 October 2021).Ethical permission for the study was provided by the University of Pretoria (ECO20-14), and this manuscript has been approved for publication by the Royal Veterinary College (PPS_01715). Permission to carry out research in the region was granted by the Northern Cape Department of Environment and Nature Conservation.; International audience; Simple SummaryDiagnostic tests used in animals are ideally extensively trialled to ensure that practitioners have confidence in the results; the ideal target should be 100% of infected animals testing positive (sensitivity), and 100% of uninfected animals testing negative (specificity). In these trials, a gold standard is necessary, against which the diagnostic tests may be compared. Commonly, tests of wild animals are not extensively trialled due to shortages of samples and the rarity of gold standard tests. This study uses samples collected for the purpose of diagnosing Mycobacterium suricattae infection in meerkats and estimates the sensitivity and specificity of available tests, both individually, and in combination. A small number of post-mortems (gold standard) were carried out, providing definitive evidence of infected animals against which to compare the tests. In addition, test results were unconventionally compared to survival times and clinical characteristics, aiming to quantify the prognostic capabilities of the tests. The study therefore not only estimates the required parameters against which to assess these tests, but also provides a model for future assessment of diagnostic tests in imperfect field scenarios. Wildlife diseases are increasingly recognised as important to society, and so methods to better quantify these are increasingly important.AbstractDiagnostic tests are used to classify individual animals’ infection statuses. However, validating test performance in wild animals without gold standard tests is extremely challenging, and the issue is further complicated in chronic conditions where measured immune parameters vary over time. Here, we demonstrate the value of combining evidence from different diagnostic approaches to aid interpretation in the absence of gold standards, large sample sizes, and controlled environments. Over a two-year period, we sampled 268 free-living meerkats (Suricata suricatta) longitudinally for Mycobacterium suricattae (a causative agent of tuberculosis), using three ante-mortem diagnostic tests based on mycobacterial culture, and antigen-specific humoral and cell-mediated immune responses, interpreting results both independently and in combination. Post-mortem cultures confirmed M. suricattae infection in 22 animals, which had prior ante-mortem information, 59% (13/22) of which were test-positive on a parallel test interpretation (PTI) of the three ante-mortem diagnostic assays (95% confidence interval: 37–79%). A similar ability to detect infection, 65.7% (95% credible interval: 42.7–84.7%), was estimated using a Bayesian approach to examine PTI. Strong evidence was found for a near doubling of the hazard of death (Hazard Ratio 1.75, CI: 1.14–2.67, p = 0.01), associated with a positive PTI result, thus demonstrating that these test results are related to disease outcomes. For individual tests, small sample sizes led to wide confidence intervals, but replication of conclusions, using different methods, increased our confidence in these results. This study demonstrates that combining multiple methodologies to evaluate diagnostic tests in free-ranging wildlife populations can be a useful approach for exploiting such valuable datasets.
Published: 2021

17. Algebraic and topological structures on rational tangles

Author: Seyed M.H. Mansourbeigi, Vida Milani, Hossein Finizadeh, and Poli Paper
Subjects: tangle convergent, Coalgebra, Structure (category theory), Bi-pseudo-module, 010103 numerical & computational mathematics, Interval (mathematics), lcsh:Analysis, Group Hopf algebra, Continued fraction, Topology, 01 natural sciences, Tangle, Interval coalgebra, Incidence algebra, Mathematics::Quantum Algebra, Physical Sciences and Mathematics, Order (group theory), 0101 mathematics, Algebraic number, Mathematics, group Hopf algebra, Computer Sciences, lcsh:Mathematics, lcsh:QA299.6-433, Tangle convergen, bi-pseudo-module, lcsh:QA1-939, Mathematics::Geometric Topology, continued fraction, 010101 applied mathematics, Algebra, incidence algebra, pseudo-tensor product, Pseudo-tensor product, Pseudo-module, pseudo-module, Geometry and Topology, tangle, Locally finite partial order, locally finite partial order, interval coalgebra
Abstract: In this paper we present the construction of a group Hopf algebra on the class of rational tangles. A locally finite partial order on this class is introduced and a topology is generated. An interval coalgebra structure associated with the locally finite partial order is specified. Irrational and real tangles are introduced and their relation with rational tangles are studied. The existence of the maximal real tangle is described in detail.
Published: 2017

18. A hybrid high-order method for flow simulations in discrete fracture networks

Author: Florent Hédin, Géraldine Pichot, Alexandre Ern, Simulation for the Environment: Reliable and Efficient Numerical Algorithms (SERENA), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique (CERMICS), École des Ponts ParisTech (ENPC), This research has been partially supported by the LABEX AMIES ANR-10-LBX-0002-01 project.The authors are grateful to the LabCom fractory (CNRS,Université de Rennes 1 and Itasca Consultants) for providing the geometry and transmissivitydata for all the DFN considered in this paper. The authors warmly thank Nicolas Pignet (EDF)for many fruitful discussions related to DiSk++. Part of the simulations presented in thispaper were carried out using the PlaFRIM experimental testbed, supported by Inria, CNRS(LABRI and IMB), Université de Bordeaux, Bordeaux INP and Conseil Régional d’Aquitaine(see https://www.plafrim.fr/)., This research has been partially supported by the LABEX AMIES ANR-10-LBX-0002-01 project., and Hédin, Florent
Subjects: Discrete fracture, Materials science, business.industry, ComputingMethodologies_SIMULATIONANDMODELING, 010103 numerical & computational mathematics, Mechanics, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], 01 natural sciences, 010101 applied mathematics, Permeability (earth sciences), Software, Flow (mathematics), Fracture (geology), 0101 mathematics, High order, business, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], ComputingMethodologies_COMPUTERGRAPHICS
Abstract: International audience; We are interested in solving flow in large trimensional Discrete Fracture Networks (DFN) with the hybrid high-order (HHO) method. The objectives of this paper are: (1) to demonstrate the benefit of using a high-order method for computing macroscopic quantities, like the equivalent permeability of fracture rocks; (2) to present the computational efficiency of our C++ software, NEF++, which implements the solving of flow in fractures based on the HHO method.
Published: 2019

19. Towards Portable Online Prediction of Network Utilization using MPI-level Monitoring

Author: Emmanuel Jeannot, Franck Cappello, Shu Mei Tseng, Bogdan Nicolae, Aparna Chandramowlishwaran, George Bosilca, University of California [Irvine] (UCI), University of California, Argonne National Laboratory [Lemont] (ANL), The University of Tennessee [Knoxville], Topology-Aware System-Scale Data Management for High-Performance Computing (TADAAM), Laboratoire Bordelais de Recherche en Informatique (LaBRI), 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, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), This research was supported by the Exascale Computing Project (17-SC-20-SC), a collaborative effort of the U.S. Department of Energy Office of Science and the National Nuclear Security Administration. This material was based upon work supported by the U.S. Department of Energy, Office of Science, under contract DE-AC02-06CH11357,and by the National Science Foundation under Grant No. #1664142. The experimentspresented in this paper were carried out using the Grid’5000/ALADDIN-G5K experimental testbed, an initiative of the French Ministry of Research through the ACI GRID incentive action, INRIA, CNRS and RENATER and other contributing partners (see http://www.grid5000.fr/)., University of California [Irvine] (UC Irvine), University of California (UC), and 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
Subjects: Artificial neural network, business.industry, Computer science, Network monitoring, Deep learning, Distributed computing, 010103 numerical & computational mathematics, 010501 environmental sciences, Prediction of resource utilization, 01 natural sciences, Timeseries forecasting, Work stealing, Online learning, Leverage (statistics), Artificial intelligence, 0101 mathematics, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], business, 0105 earth and related environmental sciences
Abstract: International audience; Stealing network bandwidth helps a variety of HPC runtimes and services to run additional operations in the background without negatively affecting the applications. A key ingredient to make this possible is an accurate prediction of the future network utilization, enabling the runtime to plan the background operations in advance, such as to avoid competing with the application for network bandwidth. In this paper, we propose a portable deep learning predictor that only uses the information available through MPI introspection to construct a recurrent sequence-to-sequence neural network capable of forecasting network utilization. We leverage the fact that most HPC applications exhibit periodic behaviors to enable predictions far into the future (at least the length of a period). Our on-line approach does not have an initial training phase, it continuously improves itself during application execution without incurring significant computational overhead. Experimental results show better accuracy and lower computational overhead compared with the state-of-the-art on two representative applications.
Published: 2019

20. Rigorous study of the equilibria of collision kernels appearing in the theory of weak turbulence

Author: Maxime Breden, Laurent Desvillettes, Technische Universität Munchen - Université Technique de Munich [Munich, Allemagne] (TUM), Université Paris Diderot, Sorbonne Paris Cité, Paris, France, Université Paris Diderot - Paris 7 (UPD7), and The research leading to this paper was partly funded by Université SorbonneParis Cité, in the framework of the 'Investissements d'Avenir', convention ANR-11-IDEX-0005. MB also acknowledges partial support from a Lichtenberg Professorship grant ofthe VolkswagenStiftung awarded to C. Kuehn.
Subjects: Keys words: weak turbulence, Complex system, 82C40, FOS: Physical sciences, Type (model theory), [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, symbols.namesake, equilibria Mathematical Subject Classification: 76F99, Mathematics - Analysis of PDEs, Mathematics (miscellaneous), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Statistical physics, 0101 mathematics, Mathematical Physics, Physics, 76P05, Turbulence, Mechanical Engineering, 010102 general mathematics, Mathematical Subject Classification: 76F99, 76P05, 82C40, Turbulence theory, Mathematical Physics (math-ph), Collision, equilibria, Functional Analysis (math.FA), Mathematics - Functional Analysis, 010101 applied mathematics, collision kernels, Boltzmann constant, Boltzmann's H-theorem, symbols, Particle, weak turbulence, Analysis, Analysis of PDEs (math.AP)
Abstract: In this paper, we rigorously obtain all the equilibria of collision kernels of type ``two particles give two particles'' appearing in weak turbulence theory under very general assumptions, thus completing the ``equality case'' in Boltzmann's H-theorem for those models. We also provide some rigorous results for collision kernels of type ``two particles give one particle'', under assumptions which include some of the most classical kernels of this type. The method of proof is inspired by the quantitative estimates obtained for the Landau equation by Desvillettes in [J. Funct. Anal. 269:1359-1403, 2015].
Published: 2018

21. Geometric optimal techniques to control the muscular force response to functional electrical stimulation using a non-isometric force-fatigue model

Author: Jérémy Rouot, Bernard Bonnard, Mathematics for Control, Transport and Applications (McTAO), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Université de Bourgogne (UB)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Centre National de la Recherche Scientifique (CNRS), Vision et Analyse de Données (LABISEN-VISION-AD), Laboratoire ISEN (L@BISEN), Institut supérieur de l'électronique et du numérique (ISEN)-YNCREA OUEST (YO)-Institut supérieur de l'électronique et du numérique (ISEN)-YNCREA OUEST (YO), This research paper benefited from the support of the FMJH Program PGMO and from thesupport of EDF, Thales, Orange and the authors are partially supported by the Labex AMIES., ANR-10-LABX-0002,AMIES,Agency for mathematics in interaction with enterprise and society(2010), and ANR: 10-LABX-0002,AMIES,Agency for mathematics in interaction with enterprise and society(2010)
Subjects: 0209 industrial biotechnology, Control and Optimization, Computer science, 02 engineering and technology, 01 natural sciences, Biomechanics fo, 020901 industrial engineering & automation, Control theory, Sampled-data co, Pulse wave, Functional electrical stimulation, Hamiltonian dif, 0101 mathematics, Applied Mathematics, Frame (networking), Dynamics (mechanics), Pulse (physics), 010101 applied mathematics, Mechanics of Materials, Variational inequality, Trajectory, Geometric optim, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Geometry and Topology, Pontryagin type, Hamiltonian (control theory)
Abstract: International audience; A recent force-fatigue parameterized mathematical model, based on the seminal contributions of V. Hill to describe muscular activity, allows to predict the muscular force response to external electrical stimulation (FES) and it opens the road to optimize the FES-input to maximize the force response to a pulse train, to track a reference force while minimizing the fatigue for a sequence of pulse trains or to follow a reference joint angle trajectory to produce motion in the non-isometric case. In this article, we introduce the geometric frame to analyze the dynamics and we present Pontryagin types necessary optimality conditions adapted to digital controls, used in the experiments, vs permanent control and which fits in the optimal sampled-data control frame. This leads to Hamiltonian differential variational inequalities, which can be numerically implemented vs direct optimization schemes.
Published: 2021

22. Multidimensional stability of V-shaped traveling fronts in time periodic bistable reaction–diffusion equations

Author: Wei-Jie Sheng, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and This paper was supported by NSF of China (11401134) and by China Scholarship Council for a one year visit of Aix Marseille Université.
Subjects: Current (mathematics), Bistability, 010102 general mathematics, Mathematical analysis, Time periodic V-shaped traveling fronts, 01 natural sciences, Stability (probability), 010101 applied mathematics, Bistable, Computational Mathematics, Computational Theory and Mathematics, Two-dimensional space, Reaction diffusion equations, Modeling and Simulation, Stability theory, Bounded function, Reaction–diffusion system, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Initial value problem, 0101 mathematics, Nonlinear Sciences::Pattern Formation and Solitons, Multidimensional stability, Mathematics
Abstract: International audience; This paper deals with the multidimensional stability of time periodic V-shaped traveling fronts in bistable reaction–diffusion equations. It is well known that time periodic V-shaped traveling fronts are asymptotically stable in two dimensional space. In the current study, we further show that such fronts are asymptotically stable under spatially decaying initial perturbations in Rn with n≥3. In particular, we show that the fronts are algebraically stable if the initial perturbations belong to L1 in a certain sense. Furthermore, we prove that there exists a solution oscillating permanently between two time periodic V-shaped traveling fronts, which implies that time periodic V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Finally we show that time periodic V-shaped traveling fronts are only time global solutions of the Cauchy problem if the initial perturbations lie between two time periodic V-shaped traveling fronts.
Published: 2016

23. A test for gene-environment interaction in the presence of measurement error in the environmental variable

Author: Hugues Aschard, Donna Spiegelman, Molin Wang, Vincent Laville, Pete Kraft, Centre de Bioinformatique, Biostatistique et Biologie Intégrative (C3BI), Institut Pasteur [Paris]-Centre National de la Recherche Scientifique (CNRS), Harvard T.H. Chan School of Public Health, The authors thank the reviewers for their helpful comments that have improved the paper. This research is supported by grant R01CA050597 from the National Cancer Institute (NCI) and R21HG007687 from the National Human Genome Research Institute (NHGRI). The authors have no conflict of interest to declare., and Institut Pasteur [Paris] (IP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: 0301 basic medicine, Epidemiology, Genome-wide association study, Breast Neoplasms, MESH: Logistic Models, Interaction, Logistic regression, 01 natural sciences, Article, Correlation, 010104 statistics & probability, 03 medical and health sciences, Bias, Statistics, Linear regression, MESH: Bias, Humans, normal discriminant analysis, MESH: Genetic Variation, MESH: Models, Genetic, 0101 mathematics, Gene–environment interaction, gene-environment interaction test, Genetics (clinical), Mathematics, [STAT.AP]Statistics [stat]/Applications [stat.AP], Observational error, MESH: Humans, Models, Genetic, Genetic Variation, Reproducibility of Results, MESH: Gene-Environment Interaction, Linear discriminant analysis, 3. Good health, MESH: Reproducibility of Results, 030104 developmental biology, Logistic Models, [SDV.GEN.GH]Life Sciences [q-bio]/Genetics/Human genetics, genome-wide association studies, MESH: Genome-Wide Association Study, Gene-Environment Interaction, [SDV.SPEE]Life Sciences [q-bio]/Santé publique et épidémiologie, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], [STAT.ME]Statistics [stat]/Methodology [stat.ME], measurement error, MESH: Breast Neoplasms, Genome-Wide Association Study
Abstract: International audience; The identification of gene-environment interactions in relation to risk of human diseases has been challenging. One difficulty has been that measurement error in the exposure can lead to massive reductions in the power of the test, as well as in bias toward the null in the interaction effect estimates. Leveraging previous work on linear discriminant analysis, we develop a new test of interaction between genetic variants and a continuous exposure that mitigates these detrimental impacts of exposure measurement error in ExG testing by reversing the role of exposure and the diseases status in the fitted model, thus transforming the analysis to standard linear regression. Through simulation studies, we show that the proposed approach is valid in the presence of classical exposure measurement error as well as when there is correlation between the exposure and the genetic variant. Simulations also demonstrated that the reverse test has greater power compared to logistic regression. Finally, we confirmed that our approach eliminates bias from exposure measurement error in estimation. Computing times are reduced by as much as fivefold in this new approach. For illustrative purposes, we applied the new approach to an ExGWAS study of interactions with alcohol and body mass index among 1,145 cases with invasive breast cancer and 1,142 controls from the Cancer Genetic Markers of Susceptibility study.
Published: 2018

24. Convergence regions for the Chebyshev–Halley family

Author: B. Campos, Jordi Canela, P. Vindel, and The authors would like to thank the anonymous referees for their suggestions and comments, which improved this paper. The first and third authors were supported by the Spanish project MTM2014-52016-C02-2-P, the Generalitat Valenciana Project PROMETEO/2016/089 and UJI project P1.1B20115-16. The second author was supported by RedIUM and MINECO (Spain) through the research network MTM2014-55580-REDT and by the mathematics institute IMAC (Castellon, Spain).
Subjects: roots, Numerical Analysis, Pure mathematics, Chebyshev–Halley family, Iterative method, polynomials, Applied Mathematics, Chebyshev systems, 010102 general mathematics, 010103 numerical & computational mathematics, dynamics, Parameter space, Fixed point, 01 natural sciences, Attraction, Chebyshev filter, Critical point (mathematics), Combinatorics, Quadratic equation, Modeling and Simulation, Polinomis, 0101 mathematics, Sistemes de Chebyshev, Mathematics
Abstract: In this paper we study the dynamical behavior of the Chebyshev–Halley methods on the family of degree n polynomials z n + c . We prove that, despite increasing the degree, it is still possible to draw the parameter space by using the orbit of a single critical point. For the methods having z = ∞ as an attracting fixed point, we show how the basins of attraction of the roots become smaller as the value of n grows. We also demonstrate that, although the convergence order of the Chebyshev–Halley family is 3, there is a member of order 4 for each value of n. In the case of quadratic polynomials, we bound the set of parameters which correspond to iterative methods with stable behaviour other than the basins of attraction of the roots.
Published: 2018

25. Through the looking glass: Indirect inference via simple equilibria

Author: Veronika Czellar, Laurent E. Calvet, emlyon business school, Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), HEC Paris Research Paper Series, and business school, emlyon
Subjects: JEL: C - Mathematical and Quantitative Methods/C.C0 - General/C.C0.C01 - Econometrics, Large class, JEL: C - Mathematical and Quantitative Methods/C.C5 - Econometric Modeling/C.C5.C53 - Forecasting and Prediction Methods • Simulation Methods, Economics and Econometrics, Hidden Markov model, long-run risk, learning, value at risk, indirect inference, particle filters, Computer science, Monte Carlo method, jel:C01, Indirect Inference, 01 natural sciences, Value at risk, Indirect inference, 010104 statistics & probability, Simple (abstract algebra), 0502 economics and business, Econometrics, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C15 - Statistical Simulation Methods: General, Capital asset pricing model, Learning, Applied mathematics, JEL: C - Mathematical and Quantitative Methods/C.C5 - Econometric Modeling/C.C5.C58 - Financial Econometrics, 050207 economics, 0101 mathematics, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, Long-run risk, jel:C53, Applied Mathematics, 05 social sciences, JEL: C - Mathematical and Quantitative Methods/C.C1 - Econometric and Statistical Methods and Methodology: General/C.C1.C13 - Estimation: General, Estimator, jel:C13, [SHS.ECO]Humanities and Social Sciences/Economics and Finance, jel:C58, jel:C15, [SHS.GESTION]Humanities and Social Sciences/Business administration, Particle filters, [SHS.GESTION] Humanities and Social Sciences/Business administration, Particle filter
Abstract: International audience; This paper proposes an indirect inference (Gourieroux, Monfort and Renault, 1993; Smith, 1993) estimation method for a large class of dynamic equilibrium models. Our approach is based on the observation that the econometric structure of these systems naturally generates auxiliary equilibria that can serve as building blocks for estimation. We use this insight to develop an accurate estimator for the long-run risk model of Bansal and Yaron (2004). We demonstrate the accuracy of our method by Monte Carlo simulation and estimate the long-run risk model on U.S. data. We also illustrate the good performance of the methodology on an asset pricing model with investor learning.
Published: 2015

26. Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

Author: Ana C. Freitas, Sandro Vaienti, Jorge Milhazes Freitas, Centro de Matemática - Universidade do Porto (CMUP), Universidade do Porto = University of Porto, Centre de Physique Théorique - UMR 7332 (CPT), Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), CPT - Ex E7 Systèmes dynamiques et théorie ergodique, Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS)-Aix Marseille Université (AMU)-Université de Toulon (UTLN)-Centre National de la Recherche Scientifique (CNRS), ACMF was partially supported by FCT (Portugal) grant SFRH/BPD/66174/2009. JMF was partially supported by FCT grant SFRH/BPD/66040/2009. All these grants are financially supported by the program POPH/FSE. ACMF and JMF were partially supported by FCT project FAPESP/19805/2014 and by CMUP (UID/MAT/00144/2013), which is funded by FCT with national (MEC) and European structural funds through the programs ,FEDER, under the partnership agreement PT2020. SV was supported by the ANRProject Perturbations and by the project Atracción de Capital Humano Avanzado del Extranjero MEC 80130047, CONICYT, at the CIMFAV, University of Valparaiso. All authors were partially supported by FCT project PTDC/MAT/12034 /2010, which is funded by national and European structural funds through the programs FEDER and COMPETE. SV is grateful to N. Haydn, M. Nicol and A. Török for several and fruitful discussions on sequential systems, especially in the framework of indifferent maps. JMF is grateful to M. Todd for fruitful discussions and careful reading of a preliminary version of this paper. All authors acknowledge the Isaac Newton Institute for Mathematical Sciences, where this work was initiated during the program Mathematics for the Fluid Earth., ANR-10-BLAN-0106,PERTURBATIONS,Perturbations aléatoires de systèmes dynamiques: applications non-uniformément dilatantes, isométries, billards et systèmes de fonctions itérées. Grandes déviations et valeurs extrêmes.(2010), Faculdade de Economia, Faculdade de Ciências, and Universidade do Porto
Subjects: Hitting Times, Statistics and Probability, Pure mathematics, Random dynamical systems, 60G70, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Dynamical Systems (math.DS), 01 natural sciences, 010104 statistics & probability, Sequential dynamical systems, FOS: Mathematics, 37A50, Mathematics - Dynamical Systems, 0101 mathematics, Extreme value theory, Mathematical Physics, Mathematics, 37A25, 37B20, Non-stationarity, Probability (math.PR), 010102 general mathematics, Mathematical Physics (math-ph), Non stationarity, Statistics, Probability and Uncertainty, Mathematics - Probability
Abstract: International audience; We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical systems, in particular to sequential dynamical systems, both given by uniformly expanding maps and by maps with a neutral fixed point, and to a few classes of random dynamical systems. Some examples are presented and worked out in detail.
Published: 2017

27. Forms of differing degrees over number fields

Author: Christopher Frei, Manfred G. Madritsch, Institut für Analysis und Computational Number Theory (Technische Universität Graz), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and For the realization of the present paper the second author received support from the Conseil Régional de Lorraine.
Subjects: Pure mathematics, Conjecture, Mathematics - Number Theory, Degree (graph theory), 11G35, 11P55, 14G05, General Mathematics, 010102 general mathematics, System of polynomial equations, Singular integral, Algebraic number field, 01 natural sciences, Ring of integers, [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], Hasse principle, 0103 physical sciences, FOS: Mathematics, Asymptotic formula, Number Theory (math.NT), 010307 mathematical physics, 0101 mathematics, Mathematics
Abstract: Consider a system of polynomials in many variables over the ring of integers of a number field $K$. We prove an asymptotic formula for the number of integral zeros of this system in homogeneously expanding boxes. As a consequence, any smooth and geometrically integral variety $X\subseteq \mathbb{P}_K^m$ satisfies the Hasse principle, weak approximation and the Manin-Peyre conjecture, if only its dimension is large enough compared to its degree. This generalizes work of Skinner, who considered the case where all polynomials have the same degree, and recent work of Browning and Heath-Brown, who considered the case where $K=\mathbb{Q}$. Our main tool is Skinner's number field version of the Hardy-Littlewood circle method. As a by-product, we point out and correct an error in Skinner's treatment of the singular integral., Comment: 23 pages; minor revision; to appear in Mathematika
Published: 2017

28. Attention, Information Processing and Choice in Incentive-Aligned Choice Experiments

Author: Olivier Toubia, Liu Yang, Martijn G. de Jong, Ecole des Hautes Etudes Commerciales (HEC Paris), HEC Paris Research Paper Series, and Business Economics
Subjects: Economics and Econometrics, choice experiments, Computer science, Process (engineering), 01 natural sciences, eye tracking, 050105 experimental psychology, Field (computer science), JEL: M - Business Administration and Business Economics • Marketing • Accounting • Personnel Economics/M.M3 - Marketing and Advertising/M.M3.M31 - Marketing, 010104 statistics & probability, 0502 economics and business, preference measurement, Econometrics, Economics, incentive alignment, 0501 psychology and cognitive sciences, JEL: C - Mathematical and Quantitative Methods/C.C9 - Design of Experiments/C.C9.C91 - Laboratory, Individual Behavior, 0101 mathematics, Business and International Management, Marketing, Choice set, Product category, 05 social sciences, Information processing, Bounded rationality, Conjoint analysis, Incentive, Respondent, JEL: C - Mathematical and Quantitative Methods/C.C8 - Data Collection and Data Estimation Methodology • Computer Programs/C.C8.C81 - Methodology for Collecting, Estimating, and Organizing Microeconomic Data • Data Access, Eye tracking, [SHS.GESTION]Humanities and Social Sciences/Business administration, 050211 marketing, Construal level theory
Abstract: In incentive-alignment choice experiments, each decision is realized with some prob- ability prob < 1. Incentive alignment induces truth telling, i.e., respondents do not consciously lie, given the information they have processed. However, based on the psychological distance literature and the bounded rationality literature, we predict that prob < 1 is not necessarily enough to induce consumers to process information and choose as they would if choices were realized with certainty (prob = 1). In three eye tracking experiments, we vary the probability prob that choices will be realized, from 0 to 1, and study the impact on attention, information processing, and choice. Consistent with our hypotheses, we find that as prob is increased from 0 to 1, consumers: process the choice-relevant information more carefully and in a way that is more consistent with a compensatory decision process; become less novelty seeking; become more price sensitive. These findings have implications for the ecological validity of incentive-aligned preference measurement surveys. While it is not feasible to systematically use questions with high prob in the eld, we further predict and find that placing a higher-probability question (such as an external validity task) at the beginning rather than the end of a questionnaire has a desirable carryover effect on attention, information processing and choice throughout the questionnaire.
Published: 2015

29. Patient specific simulation of tumor growth, response to the treatment and relapse of a lung metastasis: a clinical case

Author: Julien Jouganous, Jean Palussière, Thierry Colin, François Cornelis, Olivier Saut, Modélisation Mathématique pour l'Oncologie (MONC), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], UNICANCER-UNICANCER-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Hôpital Pellegrin, CHU Bordeaux [Bordeaux]-Groupe hospitalier Pellegrin, Institut Bergonié [Bordeaux], UNICANCER, This study has been carried out within the frame of the LABEX TRAIL, ANR-10-LABX-0057 with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the 'Investments for the future' Programme IdEx (ANR-10-IDEX-03-02).Experiments presented in this paper were carried out using the PLAFRIM experimental testbed, being developed under the Inria PlaFRIM development action with support from LABRI and IMB and other entities: Conseil R ́egional d’Aquitaine, FeDER, Universit ́e de Bordeaux and CNRS (see https://plafrim.bordeaux.inria.fr/)., Inria Bordeaux, ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Institut Bergonié [Bordeaux], and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Oncology, medicine.medical_specialty, Pathology, Radiofrequency ablation, Angiogenesis, medicine.medical_treatment, Lung metastasis, [SDV.CAN]Life Sciences [q-bio]/Cancer, 010103 numerical & computational mathematics, 01 natural sciences, law.invention, Lesion, 03 medical and health sciences, Tumor growth modeling, 0302 clinical medicine, law, Internal medicine, medicine, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Tumor growth, 0101 mathematics, Clinical data assimilation, Chemotherapy, business.industry, Partial Differential Equations, Patient specific, [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, 030220 oncology & carcinogenesis, Clinical case, Medical imaging, medicine.symptom, business
Abstract: In this paper, a parametrization strategy based on reduced order methods is presented for tumor growth PDE models. This is applied to a new simple spatial model for lung metastasis including angiogenesis. The goal is to help clinicians monitoring tumors and eventually predicting their evolution or response to a particular kind of treatment. To illustrate the whole approach, a clinical case including the natural history of the lesion, the response to a chemotherapy, and the relapse before a radiofrequency ablation is presented.
Published: 2015

30. Markov games with frequent actions and incomplete information

Author: Pierre Cardaliaguet, Catherine Rainer, Nicolas Vieille, Dinah Rosenberg, CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL-Centre National de la Recherche Scientifique (CNRS), Laboratoire de mathématiques de Brest (LM), Université de Brest (UBO)-Institut Brestois du Numérique et des Mathématiques (IBNM), Université de Brest (UBO)-Centre National de la Recherche Scientifique (CNRS), Groupement de Recherche et d'Etudes en Gestion à HEC (GREGH), Ecole des Hautes Etudes Commerciales (HEC Paris)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and HEC Paris Research Paper Series
Subjects: Mathematical optimization, Computer Science::Computer Science and Game Theory, Optimization problem, MathematicsofComputing_NUMERICALANALYSIS, jel:C00, Markov model, 01 natural sciences, Bayesian game, Markov games, Complete information, zero-sum games, 91A05, 91A15, 60J10, 0502 economics and business, incomplete information, FOS: Mathematics, 0101 mathematics, Mathematics - Optimization and Control, 050205 econometrics, Mathematics, Markov chain, Variable-order Markov model, 010102 general mathematics, 05 social sciences, Stochastic game, ComputingMilieux_PERSONALCOMPUTING, TheoryofComputation_GENERAL, stochastic, zero sum, Hamilton-Jacobi equation, repeated games, Optimization and Control (math.OC), Balance equation, [SHS.GESTION]Humanities and Social Sciences/Business administration, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Hamilton-Jacobi equations
Abstract: We study a two-player, zero-sum, stochastic game with incomplete information on one side in which the players are allowed to play more and more frequently. The informed player observes the realization of a Markov chain on which the payoffs depend, while the non-informed player only observes his opponent's actions. We show the existence of a limit value as the time span between two consecutive stages vanishes; this value is characterized through an auxiliary optimization problem and as the solution of an Hamilton-Jacobi equation.
Published: 2013
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31. Asynchronous deterministic rendezvous in bounded terrains

Author: Arnaud Labourel, Andrzej Pelc, David Ilcinkas, Jurek Czyzowicz, Département d'Informatique et d'Ingénierie (DII), Université du Québec en Outaouais (UQO), Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'informatique Fondamentale de Marseille - UMR 6166 (LIF), Université de la Méditerranée - Aix-Marseille 2-Université de Provence - Aix-Marseille 1-Centre National de la Recherche Scientifique (CNRS), See paper for details., ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), and Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest
Subjects: Computational Geometry (cs.CG), FOS: Computer and information sciences, Mathematical optimization, General Computer Science, Computer science, 0211 other engineering and technologies, Terrain, ComputerApplications_COMPUTERSINOTHERSYSTEMS, 0102 computer and information sciences, 02 engineering and technology, Computer Science::Computational Geometry, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, ComputingMethodologies_ARTIFICIALINTELLIGENCE, Theoretical Computer Science, Computer Science::Robotics, 010104 statistics & probability, mobile agent, Compass, Computer Science - Data Structures and Algorithms, rendezvous, Data Structures and Algorithms (cs.DS), 0101 mathematics, obstacle, 021103 operations research, Rendezvous, deterministic, polygon, 010201 computation theory & mathematics, Asynchronous communication, Bounded function, Obstacle, Polygon, A priori and a posteriori, Robot, Computer Science - Computational Geometry, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], Computer Science(all)
Abstract: Two mobile agents (robots) have to meet in an a priori unknown bounded terrain modeled as a polygon, possibly with polygonal obstacles. Agents are modeled as points, and each of them is equipped with a compass. Compasses of agents may be incoherent. Agents construct their routes, but the actual walk of each agent is decided by the adversary: the movement of the agent can be at arbitrary speed, the agent may sometimes stop or go back and forth, as long as the walk of the agent in each segment of its route is continuous, does not leave it and covers all of it. We consider several scenarios, depending on three factors: (1) obstacles in the terrain are present, or not, (2) compasses of both agents agree, or not, (3) agents have or do not have a map of the terrain with their positions marked. The cost of a rendezvous algorithm is the worst-case sum of lengths of the agents' trajectories until their meeting. For each scenario we design a deterministic rendezvous algorithm and analyze its cost. We also prove lower bounds on the cost of any deterministic rendezvous algorithm in each case. For all scenarios these bounds are tight.
Published: 2011

32. High-order sufficient conditions for configuration tracking of affine connection control systems

Author: María Barbero-Liñán, Mario Sigalotti, Department of Mathematics and Statistics, Queen's University [Kingston, Canada], Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), The first author acknowledges the financial support of Comissionat per a Universitats i Recerca del Departament d'Innovació, Universitats i Empresa of Generalitat de Catalunya in the final preparation of this paper., CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est
Subjects: 0209 industrial biotechnology, General Computer Science, Mechanical Engineering, Tracking, 010102 general mathematics, 02 engineering and technology, Affine connection, Motion control, 01 natural sciences, Ellipsoid, Manifold, Oscillatory controls, Mechanical system, Elliptic curve, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Control system, Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Electrical and Electronic Engineering, Forced affine connection control systems, Mathematics
Abstract: International audience; In this paper, we study under which conditions the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the literature. The sufficient conditions are expressed in terms of convex cones of vector fields defined through particular brackets of the control vector fields of the system. The tracking control laws obtained by our constructions depend on several parameters. By imposing suitable asymptotic conditions on such parameters, we construct algorithmically one-parameter tracking control laws. The theory is supported by examples of control systems associated with elliptic hovercrafts and ellipsoidal submarines.
Published: 2010

33. Connections between Theta-Graphs, Delaunay Triangulations, and Orthogonal Surfaces

Author: David Ilcinkas, Nicolas Hanusse, Nicolas Bonichon, Cyril Gavoille, Gavoille, Cyril, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-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.), See paper for details, ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007), Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), and Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest
Subjects: spanner, 0102 computer and information sciences, Delaunay triangulation, Computer Science::Computational Geometry, [INFO.INFO-CG]Computer Science [cs]/Computational Geometry [cs.CG], 01 natural sciences, law.invention, Combinatorics, symbols.namesake, law, Line graph, 0101 mathematics, Beta skeleton, Mathematics, Forbidden graph characterization, Block graph, orthogonal surface, 010102 general mathematics, theta-graph, 1-planar graph, Geometric graph theory, Planar graph, realizability, [INFO.INFO-CG] Computer Science [cs]/Computational Geometry [cs.CG], 010201 computation theory & mathematics, symbols, Topological graph theory
Abstract: International audience; $\Theta_k$-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number $k$ and the dimension of the space. TD-Delaunay graphs, a.k.a.~triangular-distance Delaunay triangulations, introduced by Chew, have been shown to be plane $2$-spanners of the 2D Euclidean complete graph, i.e., the distance in the TD-Delaunay graph between any two points is no more than twice the distance in the plane. Orthogonal surfaces are geometric objects defined from independent sets of points of the Euclidean space. Orthogonal surfaces are well studied in combinatorics (orders, integer programming) and in algebra. From orthogonal surfaces, geometric graphs, called geodesic embeddings can be built. In this paper, we introduce a specific subgraph of the $\TG$-graph defined in the 2D Euclidean space, namely the $\DTG$-graph, composed of the even-cone edges of the $\TG$-graph. Our main contribution is to show that these graphs are exactly the TD-Delaunay graphs, and are strongly connected to the geodesic embeddings of orthogonal surfaces of coplanar points in the 3D Euclidean space. Using these new bridges between these three fields, we establish: \begin{itemize} \item Every $\TG$-graph is the union of two spanning TD-Delaunay graphs. In particular, $\TG$-graphs are $2$-spanners of the Euclidean graph, and the bound of~$2$ on the stretch factor is the best possible. It was not known that $\Theta_6$-graphs are $t$-spanners for some constant $t$, and $\Theta_7$-graphs were only known to be $t$-spanners for $t \approx 7.562$. \item Every plane triangulation is TD-Delaunay realizable, i.e., every combinatorial plane graph for which all its interior faces are triangles is the TD-Delaunay graph of some point set in the plane. Such realizability property does not hold for classical Delaunay triangulations. \end{itemize}
Published: 2010

34. Euler Tour Lock-In Problem in the Rotor-Router Model

Author: Adrian Kosowski, Ralf Klasing, Evangelos Bampas, David Ilcinkas, Leszek Gąsieniec, Nicolas Hanusse, School of of Electrical and Computer Engineering [Athens] (School of E.C.E), National Technical University of Athens [Athens] (NTUA), Algorithmics for computationally intensive applications over wide scale distributed platforms (CEPAGE), Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS), Department of Computer Science [Liverpool], University of Liverpool, Laboratoire Bordelais de Recherche en Informatique (LaBRI), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB), Department of Algorithms and Systems Modelling [ETI GUT] (Gdansk University of Technology), Faculty of Electronics, Telecommunications and Informatics [GUT Gdańsk] (ETI), Gdańsk University of Technology (GUT)-Gdańsk University of Technology (GUT), See paper for details., ANR-07-BLAN-0322,ALADDIN,Algorithm Design and Analysis for Implicitly and Incompletely Defined Interaction Networks(2007), Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest, and Université de Bordeaux (UB)-École Nationale Supérieure d'Électronique, Informatique et Radiocommunications de Bordeaux (ENSEIRB)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Router, 010102 general mathematics, Eulerian path, Topology (electrical circuits), 0102 computer and information sciences, Random walk, 01 natural sciences, Complete bipartite graph, Numbering, Combinatorics, symbols.namesake, 010201 computation theory & mathematics, Bounded function, symbols, [INFO.INFO-DC]Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC], 0101 mathematics, MathematicsofComputing_DISCRETEMATHEMATICS, Mathematics, Rotor (mathematics)
Abstract: International audience; The rotor-router model, also called the Propp machine, was first considered as a deterministic alternative to the random walk. It is known that the route in an undirected graph G=(V,E), where |V|=n and |E|=m, adopted by an agent controlled by the rotor-router mechanism forms eventually an Euler tour based on arcs obtained via replacing each edge in G by two arcs with opposite direction. The process of ushering the agent to an Euler tour is referred to as the lock-in problem. In recent work [Yan03] Yanovski et al. proved that independently of the initial configuration of the rotor-router mechanism in G the agent locks-in in time bounded by 2m diam, where diam is the diameter of G. This upper bound can be matched asymptotically in lollipop graphs. In this paper we examine the dependence of the lock-in time on the initial configuration of the rotor-router mechanism. The case study is performed in the form of a game between a player pl intending to lock-in the agent in an Euler tour as quickly as possible and its adversary ad with the counter objective. First, we observe that in certain (easy) cases the lock-in can be achieved in time O(m). On the other hand we show that if adversary ad is solely responsible for the assignment of ports and pointers, the lock-in time Omega(m diam) can be enforced in any graph with m edges and diameter diam. Furthermore, we show that if ad provides its own port numbering after the initial setup of pointers by pl, the complexity of the lock-in problem is bounded by O(m min{log m,diam}). We also propose a class of graphs in which the lock-in requires time Omega(m log m). In the remaining two cases we show that the lock-in requires time Omega(m diam) in graphs with the worst-case topology. In addition, however, we present non-trivial classes of graphs with a large diameter in which the lock-in time is O(m).
Published: 2009

35. On discretization schemes for stochastic evolution equations

Author: Annie Millet, Istvan Gyongy, School of Mathematics - University of Edinburgh, University of Edinburgh, Laboratoire de Probabilités et Modèles Aléatoires (LPMA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Statistique Appliquée et MOdélisation Stochastique (SAMOS), Université Paris 1 Panthéon-Sorbonne (UP1), Modélisation Appliquée, Trajectoires Institutionnelles et Stratégies Socio-Économiques (MATISSE - UMR 8595), Université Paris 1 Panthéon-Sorbonne (UP1)-Centre National de la Recherche Scientifique (CNRS), This paper was written while I. Gyongy was visiting the University of Paris X. The research of I. Gyongy is partially supported byEU Network HARP. The research of A. Millet is partially supported by the research project BMF2003-01345, and Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Université Pierre et Marie Curie - Paris 6 (UPMC)
Subjects: Discretization, 010102 general mathematics, Probability (math.PR), Banach space, MathematicsofComputing_NUMERICALANALYSIS, Stochastic evolution, 01 natural sciences, 010101 applied mathematics, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Monotone polygon, Convergence (routing), Monotone operators, FOS: Mathematics, Applied mathematics, finite elements, 60H15 65M60, coercivity, 0101 mathematics, Analysis, Stochastic evolution equations, Mathematics - Probability, Mathematics
Abstract: International audience; Stochastic evolutional equations with monotone operators are considered in Banach spaces. Explicit and implicit numerical schemes are presented. The convergence of the approximations to the solution of the equations is proved.
Published: 2006

36. From left modules to algebras over an operad: application to combinatorial Hopf algebras

Author: Muriel Livernet, Laboratoire Analyse, Géométrie et Applications (LAGA), Université Paris 8 Vincennes-Saint-Denis (UP8)-Centre National de la Recherche Scientifique (CNRS)-Institut Galilée-Université Paris 13 (UP13), and this paper was written during the stay of the author at Institut Mittag-Leffler (djursholm, sweden).
Subjects: Pure mathematics, twisted bialgebra, 18D50 (Primary), 16W30, 16A06 (Secondary), Context (language use), 0102 computer and information sciences, Quasitriangular Hopf algebra, 01 natural sciences, Mathematics::Algebraic Topology, Mathematics::Category Theory, Mathematics::Quantum Algebra, FOS: Mathematics, S-module, 0101 mathematics, Mathematics, operad, Algebra and Number Theory, Functor, Quantum group, Applied Mathematics, 010102 general mathematics, [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA], Mathematics::Rings and Algebras, Tensor algebra, combinatorial Hopf algebra, Mathematics - Rings and Algebras, Hopf algebra, MSC2000: Primary: 18D50, Secondary: 16W30, 16A06, Rings and Algebras (math.RA), 010201 computation theory & mathematics, free associative algebra, Geometry and Topology, Forgetful functor, Analysis, Vector space
Abstract: The purpose of this paper is two fold: we study the behaviour of the forgetful functor from S-modules to graded vector spaces in the context of algebras over an operad and derive from this theory the construction of combinatorial Hopf algebras. As a byproduct we obtain freeness and cofreeness results for these Hopf algebras. Let O denote the forgetful functor from S-modules to graded vector spaces. Left modules over an operad P are treated as P-algebras in the category of S-modules. We generalize the results obtained by Patras and Reutenauer in the associative case to any operad P: the functor O sends P-algebras to P-algebras. If P is a Hopf operad then O sends Hopf P-algebras to Hopf P-algebras. If the operad P is regular one gets two different structures of Hopf P-algebras in the category of graded vector spaces. We develop the notion of unital infinitesimal P-bialgebra and prove freeness and cofreeness results for Hopf algebras built from Hopf operads. Finally, we prove that many combinatorial Hopf algebras arise from our theory, as Hopf algebras on the faces of the permutohedra and associahedra., Section 4.3 removed. To appear in Annales Math\'ematiques Blaise Pascal
Published: 2006

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