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3. Unfolding of saddle-nodes and their Dulac time

Author

Mariana Saavedra, Pavao Mardešić, Jordi Villadelprat, David Marín, 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), Departament de Matemàtiques [Barcelona] (UAB), Universitat Autònoma de Barcelona (UAB), Departamento de Matematicas, Universidad de Concepcion, Universidad de Concepción [Chile], Departament d'Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, FONDECYT. Grant number : 1120333, MINECO/FEDER. Grant number : MTM2011-26674-C02-01, MTM-2008-03437, ERDF 'A way to build Europe'. Grant number : UNAB10-4E-378, ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques(2011), Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Departament de Matemàtiques [Barcelona], Universitat Autònoma de Barcelona [Barcelona] ( UAB ), Departamento de Matematicas (Universidad de Concepcion, Chile), Universidad de Concepcion, and ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques ( 2011 )

Subjects
[ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Block (permutation group theory), Dynamical Systems (math.DS), Space (mathematics), 01 natural sciences, Combinatorics, Quadratic equation, FOS: Mathematics, Mathematics - Dynamical Systems, 0101 mathematics, Bifurcation, Saddle, Mathematics, Period function, Applied Mathematics, Unfolding of a saddle-node, 010102 general mathematics, 16. Peace & justice, 010101 applied mathematics, MSC: 34C07, Asymptotic expansions, 34C07, Node (circuits), Asymptotic expansion, Analysis
Abstract

Altres ajuts: UNAB10-4E-378, co-funded by ERDF "A way to build Europe" and by the French ANR-11-BS01-0009 STAAVF. In this paper we study unfoldings of saddle-nodes and their Dulac time. By unfolding a saddle-node, saddles and nodes appear. In the first result (Theorem A) we give a uniform asymptotic expansion of the trajectories arriving at the node. Uniformity is with respect to all parameters including the unfolding parameter bringing the node to a saddle-node and a parameter belonging to a space of functions. In the second part, we apply this first result for proving a regularity result (Theorem B) on the Dulac time (time of Dulac map) of an unfolding of a saddle-node. This result is a building block in the study of bifurcations of critical periods in a neighborhood of a polycycle. Finally, we apply Theorem A and Theorem B to the study of critical periods of the Loud family of quadratic centers and we prove that no bifurcation occurs for certain values of the parameters (Theorem C).

Published
2016
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4. Keller-Osserman estimates for some quasilinear elliptic systems

Author

Marta García-Huidobro, Cecilia S. Yarur, Marie-Françoise Bidaut-Véron, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemáticas [Santiago de Chile], Facultad de Matemáticas [Santiago de Chile], Pontificia Universidad Católica de Chile (UC)-Pontificia Universidad Católica de Chile (UC), Departamento de Matematicas y CC (Departamento de Matematicas y CC), Universidad de Santiago de Chile [Santiago] (USACH), and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Physics, Harnack inequality, Elliptic systems, a priori estimates, Applied Mathematics, 010102 general mathematics, asymptotic behaviour, Mathematics::Analysis of PDEs, A domain, Type (model theory), Quasilinear elliptic systems, 01 natural sciences, Omega, large solutions, 010101 applied mathematics, Combinatorics, Mathematics - Analysis of PDEs, 35B40, 35B45, 35J47, 35J92, 35M30, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Absorption (logic), 0101 mathematics, Analysis, Analysis of PDEs (math.AP), Harnack's inequality
Abstract

In this article we study quasilinear systems of two types, in a domain $\Omega$ of $R^N$ : with absorption terms, or mixed terms: \begin{eqnarray} (A): \mathcal{A}_{p} u=v^{\delta}, \mathcal{A}_{q}v=u^{\mu},\\ (M): \mathcal{A}_{p} u=v^{\delta}, -\mathcal{A}_{q}v=u^{\mu}, \end{eqnarray} where $\delta$, $\mu>0$ and $1 0$; the model case is $\mathcal{A}_p = \Delta_p$, $\mathcal{A}_q = \Delta_q.$ Despite of the lack of comparison principle, we prove a priori estimates of Keller-Osserman type: \begin{eqnarray} u(x)\leq Cd(x,\partial\Omega)^{-\frac{p(q-1)+q\delta}{D}},\qquad v(x)\leq Cd(x,\partial\Omega)^{-\frac{q(p-1)+p\mu}{D}}. \end{eqnarray} Concerning system $(M)$, we show that $v$ always satisfies Harnack inequality. In the case $\Omega=B(0,1)\backslash \{0\}$, we also study the behaviour near 0 of the solutions of more general weighted systems, giving a priori estimates and removability results. Finally we prove the sharpness of the results.

Published
2013
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5. Backward blow-up estimates and initial trace for a parabolic system of reaction-diffusion

Author

Marta García-Huidobro, Cecilia S. Yarur, Marie-Françoise Bidaut-Véron, Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Departamento de Matemáticas [Santiago de Chile], Facultad de Matemáticas [Santiago de Chile], Pontificia Universidad Católica de Chile (UC)-Pontificia Universidad Católica de Chile (UC), Departamento de Matematicas y CC (Departamento de Matematicas y CC), Universidad de Santiago de Chile [Santiago] (USACH), Fondcyt 7090028, 1070125,1070951, ECOS-CONICYT C08E04, and Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Trace (linear algebra), General Mathematics, Type (model theory), 01 natural sciences, Omega, Combinatorics, singularities, Mathematics - Analysis of PDEs, Reaction–diffusion system, backward estimates, 35K45, 35K57, 35K58, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Borel measure, initial trace, competitive systems, Mathematics, 010102 general mathematics, Statistical and Nonlinear Physics, Delta-v (physics), Parabolic semilinear systems of reaction-diffusion, 010101 applied mathematics, Parabolic system, Domain (ring theory), Analysis of PDEs (math.AP)
Abstract

In this article we study the positive solutions of the parabolic semilinear system of competitive type in Ω × (0, T), where Ω is a domain of ℝN, and p,q > 0, pq ≠ 1, Despite of the lack of comparison principles, we prove local upper estimates in the superlinear case pq > 1 of the form u(x, t) ≦ Ct-(p+1)/(pq-1), v(x, t) ≦ Ct-(q+1)/(pq-1) in ω × (0, T1), for any domain ω ⊂⊂ Ω, T1 ∈ (0, T), and C = C(N, p, q, T1, ω). For p, q > 1, we prove the existence of an initial trace at time 0, which is a Borel measure on Ω. Finally we prove that the punctual singularities at time 0 are removable when p, q ≧ 1 + 2/N.

Published
2010

6. CONVERGENCE IN RELATIVE ERROR FOR THE POROUS MEDIUM EQUATION IN A TUBE

Author

Audrito, Alessandro, Gárriz, Alejandro, Quirós, Fernando, Department of Mathematics - ETH, Eidgenössische Technische Hochschule - Swiss Federal Institute of Technology [Zürich] (ETH Zürich), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matematicas [Madrid], Universidad Autónoma de Madrid (UAM), European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska–Curie grant agreement 892017 (LNLFB-Problems), ANR project DEEV ANR-20-CE40-0011-01, MCIN/AEI (Spain) through projects MTM2017-87596-P, PID2020-116949GB-I00, RED2018-102650-T and the ICMAT-Severo Ochoa grant CEX2019-000904-S, and ANR-20-CE40-0011,DEEV,Modèles intégro-différentiels venant de la biologie évolutive(2020)

Subjects
Mathematics - Analysis of PDEs, Traveling waves, FOS: Mathematics, Long-time behaviour, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Porous medium diffusion in tubes, Convergence in relative error, 2010 Mathematics Subject Classification. 35K57, 35K65, 35C07, 35K55, Analysis of PDEs (math.AP)
Abstract

Given a bounded domain $D \subset \mathbb{R}^N$ and $m > 1$, we study the long-time behaviour of solutions to the Porous Medium equation (PME) posed in a tube \[ \partial_tu = Δu^m \quad \text{ in } D \times \mathbb{R}, \quad t > 0, \] with homogeneous Dirichlet boundary conditions on the boundary $\partial D \times \mathbb{R}$ and suitable initial datum at $t=0$. In two previous works, Vázquez and Gilding & Goncerzewicz proved that a wide class of solutions exhibit a traveling wave behaviour, when computed at a logarithmic time-scale and suitably renormalized. In this paper, we show that, for large times, solutions converge in relative error to the Friendly Giant, i.e., the unique nonnegative solution to the PME posed in the section $D$ of the tube (with homogeneous Dirichlet boundary conditions) having a special self-similar form. In addition, sharp rates of convergence and uniform bounds for the location of the free boundary of solutions are given.

Published
2022

7. Equivalence of Linear Complementarity Problems: Theory and Application to Nonsmooth Bifurcations

Author

MIranda-Villatoro, Felix, Castaños, Fernando, Franci, Alessio, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), 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), Departamento de Control Automático (CINVESTAV-IPN), Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Departamento de Matematicas [Mexico], Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), and Universidad Nacional Autónoma de México (UNAM)

Subjects
linear complementarity problems, nonsmooth dynamics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Mathematics::Optimization and Control, Systems and Control (eess.SY), Dynamical Systems (math.DS), Electrical Engineering and Systems Science - Systems and Control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Bifurcations, piecewise linear equations, Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Dynamical Systems, Mathematics - Optimization and Control
Abstract

Linear complementarity problems provide a powerful framework to model nonsmooth phenomena in a variety of real-world applications. In dynamical control systems, they appear coupled to a linear input-output system in the form of linear complementarity systems. Mimicking the program that led to the foundation of bifurcation theory in smooth maps, we introduce a novel notion of equivalence between linear complementarity problems that sets the basis for a theory of bifurcations in a large class of nonsmooth maps, including, but not restricted to, steadystate bifurcations in linear complementarity systems. Our definition exploits the rich geometry of linear complementarity problems and leads to constructive algebraic conditions for identifying and classifying the nonsmooth singularities associated with nonsmooth bifurcations. We thoroughly illustrate our theory on an extended applied example, the design of bistability in an electrical network, and a more theoretical one, the identification and classification of all possible equivalence classes in two-dimensional linear complementarity problems.

Published
2021

8. Modeling the Relationship Between Antibody-Dependent Enhancement and Disease Severity in Secondary Dengue Infection

Author

Lourdes Esteva, Claudia Pio Ferreira, Clémence Métayer, Felipe de Almeida Camargo, Mostafa Adimy, Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University (UNESP), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet [Saint-Étienne] (UJM)-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan [Villeurbanne] (ICJ), Departamento de Matematicas [Mexico], Universidad Nacional Autónoma de México (UNAM), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), 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), Institut Camille Jordan (ICJ), Modélisation mathématique, calcul scientifique (MMCS), Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), Université Lyon 1, UNAM, and Universidade Estadual Paulista (UNESP)

Subjects
0301 basic medicine, Local and global stability analyses for ordinary differential system, Neutralizing and enhancing antibodies, General Mathematics, Secondary infection, Immunology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Dengue virus, Biology, medicine.disease_cause, Antibodies, Viral, Severity of Illness Index, General Biochemistry, Genetics and Molecular Biology, Virus, Hemorrhagic disorder, Dengue fever, Dengue, 03 medical and health sciences, 0302 clinical medicine, medicine, Humans, Antibody-dependent enhancement, Original antigenic sin, Dengue shock syndrome (DSS), General Environmental Science, Pharmacology, Coinfection, General Neuroscience, Dengue hemorrhagic fever (DHF), Mathematical Concepts, Dengue Virus, medicine.disease, DENV1-4, Virology, Antibodies, Neutralizing, Antibody-Dependent Enhancement, 3. Good health, 030104 developmental biology, Computational Theory and Mathematics, 030220 oncology & carcinogenesis, Mathematical modeling, General Agricultural and Biological Sciences, Basic reproduction number
Abstract

Made available in DSpace on 2022-04-28T19:40:44Z (GMT). No. of bitstreams: 0 Previous issue date: 2021-08-01 Sequential infections with different dengue serotypes (DENV-1, 4) significantly increase the risk of a severe disease outcome (fever, shock, and hemorrhagic disorders). Two hypotheses have been proposed to explain the severity of the disease: (1) antibody-dependent enhancement (ADE) and (2) original T cell antigenic sin. In this work, we explored the first hypothesis through mathematical modeling. The proposed model reproduces the dynamic of susceptible and infected target cells and dengue virus in scenarios of infection-neutralizing and infection-enhancing antibody competition induced by two distinct serotypes of the dengue virus during secondary infection. The enhancement and neutralization functions are derived from basic concepts of chemical reactions and used to mimic binding to the virus by two distinct populations of antibodies. The analytic study of the model showed the existence of two equilibriums: a disease-free equilibrium and an endemic one. Using the concept of the basic reproduction numberR, we performed the asymptotic stability analysis for the two equilibriums. To measure the severity of the disease, we considered the maximum value of infected cells as well as the time when this maximum is reached. We observed that it corresponds to the time when the maximum enhancing activity for the infection occurs. This critical time was calculated from the model to be a few days after the occurrence of the infection, which corresponds to what is observed in the literature. Finally, using as output R, we were able to rank the contribution of each parameter of the model. In particular, we highlighted that the cross-reactive antibody responses may be responsible for the disease enhancement during secondary heterologous dengue infection. Inria Institut Camille Jordan Université de Lyon Université Lyon 1, 43 Bd. du 11 novembre 1918 Departamento de Matemáticas Facultad de Ciencias UNAM Institute of Biosciences São Paulo State University (UNESP) Institute of Biosciences São Paulo State University (UNESP)

Published
2021
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10. The turnpike property and the long-time behavior of the Hamilton-Jacobi-Bellman equation

Author

Esteve, Carlos, Kouhkouh, Hicham, Pighin, Dario, Zuazua, Enrique, Departemento de Matematicas, Universidad Autonoma de Madrid (UAM), Chair in Applied Analysis, Alexander von Humboldt-Professorship, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Chair of Computational Mathematics, Fundación Deusto, and Departamento de Matematicas [Madrid]

Subjects
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained controls.We prove that, when the time horizon $T$ tends to infinity, the value function asymptotically behaves as $W(x) + c\, T + \lambda$, and we provide a control interpretation of each of these three terms, making clear the link with the turnpike property.As a by-product, we obtain the long-time behavior of the solution to the associated Hamilton-Jacobi-Bellman equation in a case where the Hamiltonian is not coercive in the momentum variable. As a result of independent interest, we provide a new turnpike result for the linear-quadratic optimal control problem with constrained control. As a main feature, our turnpike result applies to the case when the steady optimum may saturate the control constraints. This prevented us from proving the turnpike property with an exponential rate, which is well-known to hold for the unconstrained case.

Published
2021

11. Rainbow polygons for colored point sets in the plane *

Author

Csaba D. Tóth, Birgit Vogtenhuber, Mikio Kano, David Orden, Jorge Urrutia, Javier Tejel, David Flores-Peñaloza, Leonardo Martínez-Sandoval, Departamento de Matematicas [Mexico], Universidad Nacional Autónoma de México (UNAM), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Ibaraki University, Instituto de Matematicas [México], Universidad de Alcalá - University of Alcalá (UAH), University of Zaragoza - Universidad de Zaragoza [Zaragoza], California State University [Northridge] (CSUN), Institute for Software Technology [Graz] (IST), and Graz University of Technology [Graz] (TU Graz)-Technische Universität Graz (TU Graz)

Subjects
Computational Geometry (cs.CG), FOS: Computer and information sciences, Discrete Mathematics (cs.DM), Boundary (topology), 0102 computer and information sciences, Computer Science::Computational Geometry, Enclosing simple polygon, 01 natural sciences, Theoretical Computer Science, Combinatorics, Colored point set, Computer Science::Discrete Mathematics, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Point (geometry), General bounds, 0101 mathematics, [MATH]Mathematics [math], Simple polygon, Mathematics, Discrete mathematics, Mathematics::Combinatorics, Particular cases, Plane (geometry), 010102 general mathematics, Rainbow, Colored, 010201 computation theory & mathematics, Polygon, Computer Science - Computational Geometry, Combinatorics (math.CO), General position, Computer Science - Discrete Mathematics
Abstract

Given a colored point set in the plane, a perfect rainbow polygon is a simple polygon that contains exactly one point of each color, either in its interior or on its boundary. Let $\operatorname{rb-index}(S)$ denote the smallest size of a perfect rainbow polygon for a colored point set $S$, and let $\operatorname{rb-index}(k)$ be the maximum of $\operatorname{rb-index}(S)$ over all $k$-colored point sets in general position; that is, every $k$-colored point set $S$ has a perfect rainbow polygon with at most $\operatorname{rb-index}(k)$ vertices. In this paper, we determine the values of $\operatorname{rb-index}(k)$ up to $k=7$, which is the first case where $\operatorname{rb-index}(k)\neq k$, and we prove that for $k\ge 5$, \[ \frac{40\lfloor (k-1)/2 \rfloor -8}{19} %Birgit: \leq\operatorname{rb-index}(k)\leq 10 \bigg\lfloor\frac{k}{7}\bigg\rfloor + 11. \] Furthermore, for a $k$-colored set of $n$ points in the plane in general position, a perfect rainbow polygon with at most $10 \lfloor\frac{k}{7}\rfloor + 11$ vertices can be computed in $O(n\log n)$ time., 23 pages, 11 figures, to appear at Discrete Mathematics

Published
2021
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22. Global null-controllability for stochastic semilinear parabolic equations

Author

Hern��ndez-Santamar��a, V��ctor, Balc'h, K��vin Le, Peralta, Liliana, Instituto de Matematicas (UNAM), Universidad Nacional Autónoma de México = National Autonomous University of Mexico (UNAM), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Departamento de Matematicas [Mexico], The work of the first author was supported by the programme 'Estancias posdoctorales por México' of CONACyT, Mexico. The second author has benefited from financial support of the French State, managed by the French National Research Agency (ANR) in the frame of the 'Investments for the future' Programme IdEx Bordeaux - SysNum (ANR-10-IDEX-03-02). The second author has also been supported by the grant 'Numerical simulation and optimal control in view of temperature regulation in smart buildings' of the Nouvelle Aquitaine Region. The second author is partially supported by the Project TRECOS ANR-20-CE40-0009 funded by the ANR (2021–2024)., ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), and ANR-20-CE40-0009,TRECOS,Nouvelles directions en contrôle et stabilisation: Contraintes et termes non-locaux(2020)

Subjects
Mathematics - Analysis of PDEs, Global null-controllability, Applied Mathematics, FOS: Mathematics, Banach fixed point method, Forward and backward semilinear stochastic parabolic equations, [MATH]Mathematics [math], Carleman estimates, Mathematical Physics, Analysis, Analysis of PDEs (math.AP)
Abstract

In this paper, we prove the small-time global null-controllability of forward (resp. backward) semilinear stochastic parabolic equations with globally Lipschitz nonlinearities in the drift and diffusion terms (resp. in the drift term). In particular, we solve the open question posed by S. Tang and X. Zhang, in 2009. We propose a new twist on a classical strategy for controlling linear stochastic systems. By employing a new refined Carleman estimate, we obtain a controllability result in a weighted space for a linear system with source terms. The main novelty here is that the Carleman parameters are made explicit and are then used in a Banach fixed point method. This allows to circumvent the well-known problem of the lack of compactness embeddings for the solutions spaces arising in the study of controllability problems for stochastic PDEs.

Published
2020

23. Erratum: 'Searches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015–2017 LIGO Data' (2019, ApJ, 879, 10)

Author

P. Kumar, B. R. Hall, R. Cavalieri, A. K. Srivastava, A. E. Pace, A. Fernandez-Galiana, A. Basti, Ryan N. Lang, J.-P. Coulon, T. Hardwick, D. Steinmeyer, E. A. Chase, Z. Frei, Piotr Jaranowski, V. Sequino, S. Caride, Jordan Camp, J. Liu, F. Travasso, Michał Bejger, A. Pasqualetti, J.-D. Fournier, M. Croquette, Philip F. Hopkins, Christian Pedersen, H. M. Lee, L. Xiao, Milan Gupta, P. Fulda, P. T.H. Pang, T. Etzel, G. Mendell, C. S. Unnikrishnan, J. Jiang, I. Fiori, S. J. Jadhav, B. C. Pant, Sourav Ghosh, Imre Bartos, V. Germain, V. Quetschke, Martin M. Fejer, R. Bork, S. Ghonge, Shawn Rosofsky, T. Di Girolamo, K. AultONeal, A. Perreca, S. M. Scott, G. Gemme, L. van der Schaaf, S. A. Pai, Cody Messick, M. Drago, L. E. Wade, Rebecca Fisher, K. S. Phukon, J. Li, J. Eichholz, Guenakh Mitselmakher, Zhihui Du, I. Belahcene, S. E. Barclay, M. Fyffe, R. Kirchhoff, R. Colgan, B. L. Pearlstone, D. M. Macleod, Charalampos Markakis, Archana Pai, W. Z. Korth, Gabriela Gonzalez, K. R. Corley, Christopher P. L. Berry, J. L. Willis, M. Eisenmann, Ofek Birnholtz, Archisman Ghosh, F. Paoletti, B. A. Boom, Samuel Deléglise, B. L. Swinkels, A. M. Sergeev, Torrey Cullen, G. Vedovato, L. E. H. Datrier, Samuele Cortese, Charlie Hoy, A. M. Holgado, G. Ciani, D. B. Kozak, A. D. Silva, J. Suresh, M. C. Milovich-Goff, J. L. Wright, Sebastiano Bernuzzi, P. Booker, S. Mastrogiovanni, Nicolas Sanchis-Gual, P. Ruggi, A. Parida, R. K. Lanza, S. S. Eikenberry, R. Pedurand, Benno Willke, S. T. Countryman, Michael E Zucker, A. Grado, Andrew Matas, C. D. Booth, D. Stocks, Surabhi Sachdev, Christopher J. Moore, Alessandra Corsi, Sanjay Kumar, V. V. Frolov, M. Fitz-Axen, Eric Howell, A. Singhal, P. Thomas, M. Arène, A. Mullavey, T. J. N. Nelson, V. Fafone, J. Betzwieser, C. Vorvick, G. Kang, Daniel E. Holz, B. J. J. Slagmolen, P. Dupej, Alena Ananyeva, Stanislav Babak, M. Constancio, C. Cahillane, Debnandini Mukherjee, C. Pankow, P. M. Meyers, S. Doravari, M. Muratore, M. C. Heintze, P. J. Sutton, Alyssa Garcia, B. Patricelli, F. Carbognani, D. S. Wu, Margaret Millhouse, J. H. Romie, G. D. O'Dea, Bruno Giacomazzo, A. Pal-Singh, S. Leavey, Hai-Ping Cheng, A. Iess, L. K. Nuttall, Erik Katsavounidis, R. Macas, G. Billingsley, S. Macfoy, O. Halim, K. W. Tsang, Kendall Ackley, R. K. Nayak, B. D. Lackey, P. Grassia, Kipp Cannon, M. Steinke, Xiaohui Fan, Richard O'Shaughnessy, B. Barr, J. Worden, Rana X. Adhikari, F. Donovan, R. Kennedy, Geoffrey Lovelace, S. G. Gaonkar, Antoine Heidmann, D. Töyrä, David Jones, Marco Cavaglia, Sascha Husa, G. Venugopalan, D.B. DeBra, A. K. Zadrożny, H. Estelles, K. Siellez, J. Derby, K. A. Thorne, Isabel Cordero-Carrión, Sung-Po Chao, H. Overmier, Eric B. Flynn, B. Gateley, G. Kuehn, Haixing Miao, H. Ohta, G. Bogaert, J. J. Bero, F. J. Raab, N. Mukund, S. Marsat, V. Tiwari, Yann Bouffanais, V. Avendano, Xiuling Li, Matthew Evans, K. L. Dooley, R. Inta, L. R. Cominsky, Rosa Poggiani, V. Frey, A. K. Mehta, S. Farinon, A. Pele, E. J. Daw, Maurizio Canepa, P. H. Nguyen, Antonio Marquina, T. A. Ferreira, M. Rakhmanov, P. Oppermann, Aaron Buikema, J. Hennig, V. Gayathri, S. Walsh, Miriam Cabero, Alessandra Buonanno, R. Metzdorff, C.-J. Haster, Gabrielle Allen, D. M. Wilken, S. Klimenko, Leo Tsukada, P. T. Baker, A. Avila-Alvarez, K. Gill, J. Palfreyman, Fangchen Feng, B. Lantz, B. Irwin, C. C. Yancey, W. G. Anderson, G. Cella, H. Vahlbruch, J. C. Mills, K. Riles, R. Mittleman, Francesco Pannarale, Soichiro Morisaki, Paul J. Groot, M. Zevin, N. A. Holland, K. Rao, Podila Satya Venkata Narasimha Sharma, K. D. Giardina, P. J. Veitch, R. De Rosa, I. Nardecchia, D. Sellers, H. Radkins, Lisa Barsotti, H. Y. Chia, Fl Linde, F. Magaña-Sandoval, M. F. Carney, C. Whittle, R. Gustafson, H. J. Bulten, Anirban Dasgupta, E. Z. Hamilton, Walter Winkler, B. P. Abbott, A. Bozzi, R. J. G. Jonker, J. K. Wofford, M. A. Page, J. Y. Vinet, H. Middleton, J. B. Kanner, Michael Keith, Robert J. McCarthy, C. C. Wipf, E. J. King, Nelson Christensen, Linqing Wen, P. Raffai, L. Naticchioni, Salvatore Vitale, A. Cumming, F. Di Renzo, Lee McCuller, N. Mazumder, J. D. E. Creighton, E. K. Gustafson, M. Weinert, H. A. G. Gabbard, S. V. Angelova, John Veitch, J. Lehmann, T. D. Abbott, J. Meidam, A. W. Heptonstall, Pablo Cerdá-Durán, Vivien Raymond, Peter R. Saulson, Alessandro Corongiu, S. Vass, S. Raja, E. Genin, J. Zhang, F. Baldaccini, L. F. Ortega, A. Rocchi, A. S. Markosyan, S. E. Strigin, J. V. Van Heijningen, H. Fong, G. Greco, J. S. Lange, F. Fidecaro, G. M. Guidi, Harald Lück, F. Marion, J. McIver, Z. Tornasi, M. J. Cowart, P. Puppo, A. L. Urban, D. Ugolini, P. Clearwater, K. E. Ramirez, D. W. Yeeles, Zoheyr Doctor, A. Malik, S. Gaudio, E. J. Fauchon-Jones, R. M. S. Schofield, R. Coyne, Fabrice Matichard, H. N. Isa, N. Arnaud, Maggie Tse, L. Wallace, A. Królak, Riccardo Sturani, J. Hanks, M. Lormand, R. Abbott, A. Ain, R. J. Trudeau, D. Moffa, J. Zweizig, C. De Rossi, D. Verkindt, C. Cocchieri, B. Goncharov, R. Birney, F. Frasconi, E. L. Merilh, M. Kinley-Hanlon, M. C. Tringali, S. Hochheim, N. A. Robertson, M. Cho, David Coward, D. Tuyenbayev, E. A. Huerta, D. J. Stops, J. S. H. Lee, Felix Wellmann, R. Flaminio, J. Warner, J. J. McCann, T. J. Slaven-Blair, S. ShyamSundar, C. Stachie, R. Frey, Duncan Meacher, N. V. Keerthana, Moritz Mehmet, Benjamin J. Owen, R. Passaquieti, J. F. J. van den Brand, E. A. Muñiz, K. Y. Ng, S. Brunett, Marco Romanelli, E. K. Wessel, Vijay Varma, M. MacInnis, C. Rajan, J. K. Blackburn, Bala R. Iyer, Terry G. McRae, E. Chassande-Mottin, S. P. Stevenson, Sebastian Steinlechner, Sheila Rowan, S. Caudill, G. Gaur, S. C. McGuire, J. F. Read, Chris A. Collins, J. G. Bartlett, Márton Tápai, W. Ren, Mandar Patil, Abhirup Ghosh, Sheon Chua, S. Sunil, M. Tacca, Martin Hendry, Cecilio García-Quirós, R. Bonnand, S. Di Pace, Mariana Fazio, A. Dmitriev, G. Koekoek, A. J. Weinstein, R. Goetz, S. Katsanevas, V. Boschi, Marcus E. Lower, Tarun Souradeep, M. Yvert, S. Ponrathnam, B. U. Gadre, M. Pürrer, S. Kwang, C. L. Romel, M. C. Díaz, Sebastien Biscans, G. A. Prodi, J. C. Barayoga, S. McCormick, P. Rapagnani, T. Mistry, A. L. Stuver, D. Hoak, D. Sentenac, A. Bisht, R. DeSalvo, Karsten Danzmann, N. Letendre, L. G. Prokhorov, Patrick Brady, Nikhil Sarin, D. Passuello, Odylio D. Aguiar, I. W. Martin, C. F. Da Silva Costa, Hua Wang, M. van Beuzekom, Liam Cunningham, M. Punturo, Leopoldo Milano, K. Haris, Madeline Wade, M. Di Giovanni, P. Leaci, L. Glover, S. A. Bilgili, Jay D. Tasson, S. Mitra, A. W. Jones, H. S. Chen, M. Landry, R. De Pietri, S. Biscoveanu, Rocco Romano, A. Cirone, P. Couvares, F. Garufi, David H. Shoemaker, S. Karki, Junwei Cao, O. V. Palashov, Sean T. McWilliams, Y. Boetzel, Hongyu Shen, Nicholas Demos, J. D. Lough, D. C. Coyne, Colm Talbot, Andreas Freise, M. Boer, M. A. Okada, Shubhanshu Tiwari, A. F. Brooks, P. J. Quinonez, F. Piergiovanni, Slawomir Gras, D. Lumaca, M. Haney, K. Mason, L. Di Fiore, B. Mours, Jingbo Wang, Soma Mukherjee, E. C. Ferreira, Sanjeev Dhurandhar, G. Wang, Hyun Lee, S. W. S. Ng, John D. Scott, M. Standke, Otto A. Hannuksela, Surendra Nadh Somala, C. Austin, N. Radulescu, Patrick Godwin, R. A. Mercer, M. Barsuglia, Jan Harms, A. S. Sengupta, J. Calderón Bustillo, K. Izumi, T. Sadecki, Paul D. Lasky, Kiran Prasai, J. W. Westhouse, T. A. Callister, Matthew Pitkin, Denis Martynov, Marco Bazzan, Xin Chen, R. M. Martin, David A. Nichols, W. Katzman, S. Grunewald, R. Prasanna, Edward K. Porter, D. Buskulic, G. Giordano, K. Toland, D. J. Hofman, C. Ingram, L. Pinard, G. L. Mansell, I. Maksimovic, S. Ossokine, Jinsook Kim, R. L. Ward, G. Hemming, C. Affeldt, L. Matone, M. Davier, M. C. Araya, Srishti Tiwari, C. Lazzaro, Patricia Schmidt, V. Brisson, M. J. Yap, Lindsay DeMarchi, C. K. Cheong, Hyang Woon Lee, A. Grant, John R. Smith, C. Palomba, S. Privitera, Matthew Kerr, M. Khursheed, A. Possenti, Federico Ferrini, F. Brighenti, Jade Powell, B. B. Lane, A. Viceré, Lucas Guillemot, C. Messenger, L. Kuo, H. Yamamoto, Lijing Shao, G. Vajente, E. Capocasa, S. M. Gaebel, José A. Font, N. Singh, J. P. Zendri, G. Rutins, Graham Woan, R. Taylor, Robert L. Byer, Stuart Reid, M. S. Shahriar, Tyson Littenberg, T. D. Creighton, L. Zhang, J. H. Klika, S. Barnum, James Healy, P. A. Altin, Haocun Yu, M. Hulko, V. Mangano, Riccardo Ciolfi, Yi Chen, B. W. Schulte, M. Granata, J. C. Driggers, A. Schönbeck, Alexander C. Jenkins, B. Rajbhandari, P. Brockill, M. Nery, Ettore Majorana, A. A. Ciobanu, S. A. Usman, Y. K. Lecoeuche, G. M. Harry, Maya Fishbach, K. W. Chung, S. Ascenzi, V. Kringel, F. J. Hayes, M. Agathos, M. Kasprzack, E. Cuoco, Jacob Scheuer, Binlei Ding, S. M. Koehlenbeck, Gregorio Carullo, G. Pagano, S. Appert, Y. Setyawati, Roman Schnabel, L. Sammut, Daniel Wysocki, J. E. Brau, A. A. van Veggel, D. Fiorucci, A. K. Prajapati, A. Gupta, S. Meshkov, Seog Oh, N. Leroy, R. L. Savage, Efim A. Khazanov, G. Ballardin, A. S. Bell, M. Laxen, D. Barker, A. Samajdar, Michael L. Gorodetsky, Vuk Mandic, Minchuan Zhou, H. K. Gulati, David H. Reitze, Rahul Kashyap, A. Markowitz, Ryan Lynch, J. Prasad, Alessandro Ridolfi, B. Bécsy, M. Bawaj, Alessandro Bertolini, Q. Chu, Bernard F. Schutz, Li Ju, C. Buy, M. Oliver, Daniel A. Shaddock, Brittany Kamai, G. Dálya, A. Giazotto, P. Shawhan, Lionel London, F. Aubin, A. R. Wade, I. Ferrante, G. Stratta, C. M. Mow-Lowry, Sergey P. Vyatchanin, F. Y. Khalili, D. C. Vander-Hyde, Alejandro Torres-Forné, A. Allocca, P. Ehrens, Paul M. Ricker, Jesper Munch, H. Khan, G. Valdes, Steven Bloemen, R. Tso, K. Venkateswara, R. Cotesta, D. J. McManus, Jonathan R. Gair, C. Horst, F. Lin, Alice K. Harding, Tania Regimbau, S. B. Anderson, J.-G. Ducoin, Tim Dietrich, C. V. Kalaghatgi, J. Hanson, A. Miller, N. Koper, L. Mereni, B. Idzkowski, V. Loriette, L. Aiello, M. Gosselin, R. Green, Vivishek Sudhir, Rico K. L. Lo, E. E. Cowan, B. F. Whiting, E. Schreiber, J. Casanueva Diaz, S. D. Linker, B. Pang, R. Robie, A. Hreibi, Tristan Briant, V. Skliris, L. Sun, Marta Colleoni, William Parker, N. A. Lockerbie, R. C. Walet, Patrick M. Koch, J. Neilson, P. Charlton, J. A. Giaime, Kejia Lee, Mark A. Scheel, F. Clara, A. K. Lenon, Alberto Vecchio, Y. M. Kim, J. M. Fishner, Maher Yazback, Zachariah B. Etienne, V. P. Mitrofanov, S. Kaufer, S. Banagiri, H. Qi, L. Magaña Zertuche, Lili Yang, Hang Yu, N. Bode, P. Schale, Leo Singer, Achamveedu Gopakumar, C. Van Den Broeck, E. Sowell, A. M. Sintes, M. A. Aloy, M. Bitossi, G. Bergmann, K. Wette, M. De Laurentis, W. Del Pozzo, P. F. Cohadon, H. Heitmann, Carlos O. Lousto, T. Prestegard, T. L. Lam, O. J. Piccinni, Keith C. Gendreau, J. S. Areeda, K. Bossie, Tomasz Bulik, Will M. Farr, M. Montani, Jennifer Watchi, Miftar Ganija, T. P. Downes, Rainer Weiss, K. A. Santiago, F. Ricci, M. Branchesi, Gilles Theureau, M. Was, D. Huet, S. H. Huttner, M. H. Wimmer, A. Effler, Dániel Barta, A. Kumar, V. Srivastava, M. Fays, M. M. Hanke, Alessandro Longo, Hartmut Grote, Chandra Kant Mishra, R. Bhandare, Ryan Magee, John J. Oh, Timothy Evans, C. North, Thomas Dent, P. Corban, M. C. Edwards, S. C. Tait, Nancy Aggarwal, Zahoor Ali Khan, M. Pedraza, M. Chan, Richard J. Oram, L. Trozzo, D. Y. T. Pong, E. Massera, A. Di Lieto, Matthew Bailes, S. J. Chamberlin, M. Vasúth, Zifan Zhou, P. Ajith, Jonathan Cripe, C-H. Lee, Andrew Melatos, M. Lorenzini, I. A. Bilenko, L. Haegel, G. Losurdo, David J. Ottaway, E. Bonilla, Robert Stone, Rory Smith, C. Adams, Kazuhiro Agatsuma, Alessandro Nagar, A. Mishkin, A. Paoli, F. Cavalier, T. Enoto, H. Vocca, S. J. Kapadia, P. B. Covas, Frank Ohme, Eugeniy E. Mikhailov, V. Bossilkov, D. B. Tanner, Edward Seidel, Albert Lazzarini, O. E. S. Sauter, J. H. Briggs, Mark Hannam, F. Thies, X. Liu, R. M. Blair, D. Sigg, S. W. Ballmer, D. M. Shoemaker, M. Tonelli, François Bondu, A. Gennai, Rahul Kumar, Harald P. Pfeiffer, J. M. Gonzalez Castro, I. Dave, B. D. Cheeseboro, G. Cerretani, P. J. Easter, Kevin M. Ryan, M. Korobko, J. Woehler, Tanja Hinderer, F. Badaracco, Michelle E. Walker, Samaya Nissanke, M. Fletcher, B. Hughey, Zaven Arzoumanian, A. Ramos-Buades, A. R. Williamson, A. Strunk, S. L. Danilishin, M. Rizzo, B. K. Berger, Olivier Minazzoli, Devon S. Johnson, David Cohen, David E. McClelland, T. Huynh-Dinh, P. Weltervrede, Chunglee Kim, David Blair, S. D'Antonio, S. Chung, N. Kijbunchoo, Sheelu Abraham, G. Moreno, W. A. Campbell, A. Kontos, K. Rose, N. N. Janthalur, N. V. Krishnendu, J. Junker, S. Sitmukhambetov, Ismaël Cognard, J. S. Kissel, H. Cao, D. J. Vine, S. Penn, A. C. Green, Neil J. Cornish, D. Rosińska, M. Razzano, P. G. Murray, G. Mo, B. Sassolas, C. Fee, Andrew Lundgren, G. Cho, W. S. Kim, Marc Favata, Xing-Jiang Zhu, Patrice Hello, Kevin Barkett, J. Birch, S. Bae, S. E. Gossan, Roger Jones, V. J. Roma, C. J. Richardson, J. M. Isac, A. P. Spencer, Fausto Acernese, A. Chiummo, V. Dattilo, Edwin J. Son, E. Coccia, C. Graef, B. A. Weaver, J. G. Rollins, L.-W. Wei, Felice Sorrentino, D. Moraru, C. Gray, G. H. Ogin, D. D. Brown, Gianpietro Cagnoli, Fabien Kéfélian, J. H. Hough, P. W. F. Forsyth, Anthony A. Amato, N. van Bakel, Stefan Hild, Y. Ma, I. Dorrington, S. R. Thondapu, J. R. Palamos, I. Di Palma, F. Martelli, Karan Jani, R. Shink, E. Goetz, Giuseppe Intini, R. A. Eisenstein, T. J. Shaffer, A. Masserot, Yuri Levin, M. Mantovani, E. A. Quintero, A. Brillet, K. Kawabe, S. M. Aston, A. Trovato, Luca Gammaitoni, M. B. Shaner, L. Rei, Huang-Wei Pan, Gijs Nelemans, S. B. Coughlin, Jessica Steinlechner, A. Neunzert, F. Vetrano, R. Gray, S. Antier, E. D. Hall, Michael W. Coughlin, I. Khan, M. Heurs, Reed Essick, S. Kandhasamy, S. E. Dwyer, David Keitel, Hee-Suk Cho, Michele Zanolin, Benjamin Stappers, G. D. Meadors, S. J. Cooper, B. Sorazu, A. Kutynia, A. Lartaux-Vollard, Suvadeep Bose, R. Gouaty, Andrea Chincarini, M. K. M. Bader, T. Z. Summerscales, K. Holt, Z. Márka, S. Koley, M. Brinkmann, E. Cesarini, T. Zelenova, M. Merzougui, Riccardo Bassiri, Magnus Manske, D. Pascucci, T. J. Massinger, T. Vo, O. Chaibi, V. Kalogera, V. Sandberg, Koh Ueno, S. Frasca, E. Maros, Jonathan Richardson, S. Márka, N. Sennett, Kai Staats, L. Conti, G. D. Hammond, Javed Rana, M. Chaturvedi, Jimin George, M. Sieniawska, Martin Obergaulinger, Wynn C. G. Ho, P. Weßels, T. Dal Canton, Stephen Fairhurst, Carl Blair, K. Chakravarti, Fabio Marchesoni, S. G. Crowder, J. Bosveld, Kyungmin Kim, Debarati Chatterjee, B. O'Reilly, P. Gruning, L. Rolland, Fabrizio Barone, N. Man, K. A. Strain, Peter Aufmuth, K. Haughian, László Á. Gergely, A. Macquet, Daichi Tsuna, D. Talukder, David A. Williams, I. W. Harry, Z. A. Warden, K. Mogushi, John A. Clark, Ben Farr, P. J. King, J. T. Whelan, K. H. Lai, Aaron Viets, J. Feicht, Christophe Collette, C. J. Perez, B. D. O'Brien, O. Puncken, Joey Shapiro Key, J. R. Sanders, Marek Szczepanczyk, C. Bradaschia, Ik Siong Heng, A. Rüdiger, A. L. Miller, K. S. Karvinen, P. Astone, Mairi Sakellariadou, G. Pillant, S. H. R. Yuen, O. de Varona, Tenglin Li, I. Kowalska, D. Estevez, Marie-Anne Bizouard, Fabian Jankowski, Nergis Mavalvala, Jerome Degallaix, C. Casentini, Sebastian Khan, B. C. Barish, V. Kondrashov, Arunava Mukherjee, Y. Minenkov, P. Bacon, J. C. Bayley, H. Wittel, M. Deenadayalan, S. G. Schwalbe, M. Phelps, R. G. Ormiston, F. Cipriano, Michael Thomas, P. Popolizio, Koji Arai, E. J. Sanchez, A. G. Lyne, M. Vardaro, F. Robinet, F. Cleva, M. P. Ross, T. B. Edo, M. Pichot, Maximiliano Isi, E. M. Gretarsson, Ying Guo, D. Beniwal, Peter Fritschel, Wenxiao Wang, M. Masso-Reid, L. E. Sanchez, Enrico Calloni, G. Traylor, Thomas Corbitt, L. Salconi, C. A. Costa, Paulo C. C. Freire, Slavko Bogdanov, Laura Cadonati, D. A. Steer, L. Kleybolte, Daniel R. George, Chad Hanna, A. Bramley, C. Kimball, J. Oberling, M. Pirello, S. R.P. Mohapatra, J. Bidler, F. Nocera, C. Zhao, Kun Li, T. Zhang, Thibaut Jacqmin, C. I. Torrie, M. Saleem, Douglas Davis, Geraint Pratten, H. Fair, Andrea Taracchini, D. Bersanetti, G. Ashton, Yu Wang, Francisco Hernandez Vivanco, Eric Thrane, C. Michel, T. D. Knowles, R. Quitzow-James, V. B. Adya, Laser Interferometer Gravitational-Wave Observatory (LIGO), Louisiana State University, Baton Rouge, Inter-University Centre for Astronomy and Astrophysics (IUCAA), Università di Salerno, School of Physics, Monash University, Max Planck Institute for Gravitational Physics, University of Cambridge, University of Birmingham, Instituto Nacional de Pesquisas Espaciais (INPE), Gran Sasso Science Institute, INFN, International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bengaluru 560089, India, NCSA, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA, Universita di Pisa, I-56127 Pisa, Italy, Universitat de València (UV), Australian National University, Laboratoire des matériaux avancés (LMA), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA, Scottish Universities Physics Alliance (SUPA), Laboratoire de l'Accélérateur Linéaire (LAL), Université Paris-Sud - Paris 11 (UP11)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS), California State University Fullerton, AstroParticule et Cosmologie (APC (UMR_7164)), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), European Gravitational Observatory (EGO), Università di Roma Tor Vergata, INFN, Sezione di Roma, I-00185 Roma, Italy, Laboratoire d'Annecy de Physique des Particules (LAPP), Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS), Institut für Erdmessung, Leibniz Universität Hannover, Embry-Riddle Aeronautical University (ERAU), Montclair State University, Montclair, NJ 07043, USA, National Institute for Subatomic Physics (NIKHEF), Korea Advanced Institute of Science and Technology, Swinburne University of Technology, Department of Physics, West Virginia University (WVU), Università degli Studi di Perugia = University of Perugia (UNIPG), Syracuse University, University of Minnesota, California Institute of Technology, Department of Astronomy (CALTECH), KFKI Research Institute for Particle and Nuclear Physics (KFKI-RMKI), University of Florida, Stanford University, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia (INFN), Dipartimento di Fisica e Astronomia G. Galilei, Università di Padova, Department of Physics, Montana State University, Centrum Astronomiczne im. M. Kopernika, Warszawa (CAMK), University of Adelaide, Friedrich-Schiller-Universität Jena, Rochester Institute of Technology, Center for Interdisciplinary Exploration and Research in Astrophysics, Department of Physics and Astronomy, Northwestern University, Istituto Nazionale di Fisica Nucleare, Sezione di Genova (INFN), RRCAT, Indore, Madhya Pradesh 452013, India, Faculty of Physics, M.V. Lomonosov Moscow State University, Istituto Nazionale di Fisica Nucleare, Sezione di Pisa (INFN), The University of Western Australia (UWA), Institute for Mathematics, Astrophysics, and Particle Physics, Department of Astrophysics, Radboud University (IMAPP), Astrophysique Relativiste Théories Expériences Métrologie Instrumentation Signaux (ARTEMIS), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de la Côte d'Azur, COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Université Côte d'Azur (UCA)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Physik-Institut, Universität Zürich, Centre National de la Recherche Scientifique (CNRS), Cardiff University, Department of Physics, University of Oregon, Laboratoire Kastler Brossel (LKB (Jussieu)), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Urbino 'Carlo Bo', Astronomical Observatory, Warsaw University, Center for Relativistic Astrophysics, School of Physics, Georgia Institute of Technology, Université de Lyon, Istituto Nazionale di Fisica Nucleare, Sezione di Napoli (INFN), NASA/Goddard Space Flight Center (NASA/GSFC), University of Tokyo, Tsinghua University, Texas Tech University, Lubbock, TX 79409, USA, University of Mississippi, Istituto Nazionale di Fisica Nucleare, Sezione di Roma Tor Vergata (INFN), The Pennsylvania State University, University Park, PA 16802, USA, University of New South Wales, University of Chicago, Department of Physics, University of Hong Kong, Department of Physics and Astronomy, Seoul National University, Pusan National University, University of Maryland, Carleton College, Northfield, INAF, Osservatorio Astronomico di Padova, I-35122 Padova, Italy, School of Physics, University of Melbourne, Columbia University, New York, Department de Física, Universitat de les Illes Balears, Université Libre de Bruxelles, Department of Physics and Astronomy, Sonoma State University, Istituto Nazionale di Fisica Nucleare, Sezione di Padova (INFN), Departamento de Matematicas, Universitat de Valencia, E-46100 Burjassot, Valencia, Spain, University of Rhode Island, Kingston, RI 02881, USA, The University of Texas Rio Grande Valley, Brownsville, TX 78520, USA, Bellevue College, Bellevue, WA 98007, USA, Eötvös Loránd University (ELTE), Raman Research Institute, Duke University [Durham], INFN, Sezione di Milano Bicocca, Gruppo Collegato di Parma, I-43124 Parma, Italy, California State University, San Bernardino, INFN, Trento Institute for Fundamental Physics and Applications, I-38123 Povo, Trento, Italy, Colorado State University, Fort Collins, Kenyon College, Gambier, OH 43022, USA, National Astronomical Observatory of Japan (NAOJ), Canadian Institute for Theoretical Astrophysics, McLennan Physical Laboratories, University of Toronto (CITA), University of Edinburgh, Indian Institute of Technology, University of Szeged [Szeged], Tata Institute of Fundamental Research (TIFR), University of Michigan, Washington State University, Washington University in Saint Louis (WUSTL), Department of Physics and Astronomy, University of Missouri, Directorate of Construction, Services & Estate Management, Mumbai 400094, India, Bialystok University, Physics Department, King's College London, Strand, University of Southampton, Institute of Applied Physics, Ewha Womans University, Inje University Gimhae, South Gyeongsang 50834, Republic of Korea, National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea, Institut für Theoretische Physik, Universität Hamburg, Chennai Mathematical Institute, National Centre for Nuclear Research (NCBJ), Center for Radiophysics and Space Research, Cornell University (CRSR), Hillsdale College, Hillsdale, MI 49242, USA, Korea Astronomy and Space Science Institute (KASI), Marshall Space Flight Center, NASA, Dipartimento di Matematica e Fisica, Università del Salento, Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL), University of Portsmouth, Portsmouth, PO1 3FX, UK, Southern University and A& M College, Baton Rouge, LA 70813, USA, College of William and Mary, Williamsburg, Centre Scientifique de Monaco, 8 quai Antoine Ier, MC-98000, Monaco, Museo Storico della Fisica e Centro Studi e Ricerche ?Enrico Fermi,? 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Howell, Ej, Hoy, Cg, Huang, Y, Hubner, Mt, Huerta, Ea, Huet, D, Hughey, B, Hui, V, Husa, S, Huttner, Sh, Huynh-Dinh, T, Idzkowski, B, Iess, A, Inchauspe, H, Ingram, C, Inta, R, Intini, G, Irwin, B, Isa, Hn, Isac, Jm, Isi, M, Iyer, Br, Jacqmin, T, Jadhav, Sj, Jani, K, Janthalur, Nn, Jaranowski, P, Jariwala, D, Jenkins, Ac, Jiang, J, Johnson, D, Jones, Aw, Jones, Di, Jones, Jd, Jones, R, Jonker, Rjg, Ju, L, Junker, J, Kalaghatgi, Cv, Kalogera, V, Kamai, B, Kandhasamy, S, Kang, G, Kanner, Jb, Kapadia, Sj, Karki, S, Kashyap, R, Kasprzack, M, Katsanevas, S, Katsavounidis, E, Katzman, W, Kaufer, S, Kawabe, K, Keerthana, Nv, Kefelian, F, Keitel, D, Kennedy, R, Key, J, Khalili, Fy, Khan, I, Khan, S, Khazanov, Ea, Khetan, N, Khursheed, M, Kijbunchoo, N, Kim, C, Kim, Jc, Kim, K, Kim, W, Kim, Ym, Kimball, C, King, Pj, Kinley-Hanlon, M, Kirchhoff, R, Kissel, J, Kleybolte, L, Klika, Jh, Klimenko, S, Knowles, Td, Koch, P, Koehlenbeck, Sm, Koekoek, G, Koley, S, Kondrashov, V, Kontos, A, Koper, N, Korobko, M, Korth, Wz, Kovalam, M, Kozak, Db, Kramer, C, Kringel, V, Krishnendu, N, Krolak, A, Krupinski, N, Kuehn, G, Kumar, A, Kumar, P, Kumar, R, Kuo, L, Kutynia, A, Kwang, S, Lackey, Bd, Laghi, D, Lai, Kh, Lam, Tl, Landry, M, Lane, Bb, Lang, Rn, Lange, J, Lantz, B, Lanza, Rk, Lartaux-Vollard, A, Lasky, Pd, Laxen, M, Lazzarini, A, Lazzaro, C, Leaci, P, Leavey, S, Lecoeuche, K, Lee, Ch, Lee, Hk, Lee, Hm, Lee, Hw, Lee, J, Lee, K, Lehmann, J, Lenon, Ak, Leroy, N, Letendre, N, Levin, Y, Li, A, Li, J, Li, Kjl, Li, Tgf, Li, X, Lin, F, Linde, F, Linker, Sd, Littenberg, Tb, Liu, J, Liu, X, Llorens-Monteagudo, M, Lo, Rkl, London, Lt, Longo, A, Lorenzini, M, Loriette, V, Lormand, M, Losurdo, G, Lough, Jd, Lousto, Co, Lovelace, G, Lower, Me, Luck, H, Lumaca, D, Lundgren, Ap, Lynch, R, Ma, Y, Macas, R, Macfoy, S, Macinnis, M, Macleod, Dm, Macquet, A, Hernandez, Im, Magana-Sandoval, F, Magee, Rm, Majorana, E, Maksimovic, I, Malik, A, Man, N, Mandic, V, Mangano, V, Mansell, Gl, Manske, M, Mantovani, M, Mapelli, M, Marchesoni, F, Marion, F, Marka, S, Marka, Z, Markakis, C, Markosyan, A, Markowitz, A, Maros, E, Marquina, A, Marsat, S, Martelli, F, Martin, Iw, Martin, Rm, Martinez, V, Martynov, Dv, Masalehdan, H, Mason, K, Massera, E, Masserot, A, Massinger, Tj, Masso-Reid, M, Mastrogiovanni, S, Matas, A, Matichard, F, Matone, L, Mavalvala, N, Mccann, Jj, Mccarthy, R, Mcclelland, De, Mccormick, S, Mcculler, L, Mcguire, Sc, Mcisaac, C, Mciver, J, Mcmanus, Dj, Mcrae, T, Mcwilliams, St, Meacher, D, Meadors, Gd, Mehmet, M, Mehta, Ak, Meidam, J, Villa, Em, Melatos, A, Mendell, G, Mercer, Ra, Mereni, L, Merfeld, K, Merilh, El, Merzougui, M, Meshkov, S, Messenger, C, Messick, C, Messina, F, Metzdorff, R, Meyers, Pm, Meylahn, F, Miani, A, Miao, H, Michel, C, Middleton, H, Milano, L, Miller, L, Millhouse, M, Mills, Jc, Milovich-Goff, Mc, Minazzoli, O, Minenkov, Y, Mishkin, A, Mishra, C, Mistry, T, Mitra, S, Mitrofanov, Vp, Mitselmakher, G, Mittleman, R, Mo, G, Moffa, D, Mogushi, K, 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Passaquieti, R, Passuello, D, Patil, M, Patricelli, B, Payne, E, Pearlstone, Bl, Pechsiri, Tc, Pedersen, Aj, Pedraza, M, Pedurand, R, Pele, A, Penn, S, Perego, A, Perez, Cj, Perigois, C, Perreca, A, Petermann, J, Pfeiffer, Hp, Phelps, M, Phukon, K, Piccinni, Oj, Pichot, M, Piergiovanni, F, Pierro, V, Pillant, G, Pinard, L, Pinto, Im, Pirello, M, Pitkin, M, Plastino, W, Pong, Dyt, Ponrathnam, S, Popolizio, P, Porter, Ek, Powell, J, Prajapati, Ak, Prasad, J, Prasai, K, Prasanna, R, Pratten, G, Prestegard, T, Principe, M, Prodi, Ga, Prokhorov, L, Punturo, M, Puppo, P, Purrer, M, Qi, H, Quetschke, V, Quinonez, Pj, Raab, Fj, Raaijmakers, G, Radkins, H, Radulesco, N, Raffai, P, Raja, S, Rajan, C, Rajbhandari, B, Rakhmanov, M, Ramirez, Ke, Ramos-Buades, A, Rana, J, Rao, K, Rapagnani, P, Raymond, V, Razzano, M, Read, J, Regimbau, T, Rei, L, Reid, S, Reitze, Dh, Rettegno, P, Ricci, F, Richardson, Cj, Richardson, Jw, Ricker, Pm, Riemenschneider, G, Riles, K, Rizzo, M, Robertson, Na, Robinet, F, Rocchi, A, Rolland, L, Rollins, Jg, Roma, Vj, Romanelli, M, Romano, R, Romel, Cl, Romie, Jh, Rose, Ca, Rose, D, Rose, K, Rosinska, D, Rosofsky, Sg, Ross, Mp, Rowan, S, Rudiger, A, Ruggi, P, Rutins, G, Ryan, K, Sachdev, S, Sadecki, T, Sakellariadou, M, Salafia, O, Salconi, L, Saleem, M, Samajdar, A, Sammut, L, Sanchez, Ej, Sanchez, Le, Sanchis-Gual, N, Sanders, Jr, Santiago, Ka, Santos, E, Sarin, N, Sassolas, B, Saulson, Pr, Sauter, O, Savage, Rl, Schale, P, Scheel, M, Scheuer, J, Schmidt, P, Schnabel, R, Schofield, Rm, Schonbeck, A, Schreiber, E, Schulte, Bw, Schutz, Bf, Scott, J, Scott, Sm, Seidel, E, Sellers, D, Sengupta, A, Sennett, N, Sentenac, D, Sequino, V, Sergeev, A, Setyawati, Y, Shaddock, Da, Shaffer, T, Shahriar, M, Shaner, Mb, Sharma, A, Sharma, P, Shawhan, P, Shen, H, Shink, R, Shoemaker, Dh, Shoemaker, Dm, Shukla, K, Shyamsundar, S, Siellez, K, Sieniawska, M, Sigg, D, Singer, Lp, Singh, D, Singh, N, Singhal, A, Sintes, Am, Sitmukhambetov, S, Skliris, V, Slagmolen, Bjj, Slaven-Blair, Tj, Smith, Jr, Smith, Rje, Somala, S, Son, Ej, Soni, S, Sorazu, B, Sorrentino, F, Souradeep, T, Sowell, E, Spencer, Ap, Spera, M, Srivastava, Ak, Srivastava, V, Staats, K, Stachie, C, Standke, M, Steer, Da, Steinke, M, Steinlechner, J, Steinlechner, S, Steinmeyer, D, Stevenson, Sp, Stocks, D, Stone, R, Stops, Dj, Strain, Ka, Stratta, G, Strigin, Se, Strunk, A, Sturani, R, Stuver, Al, Sudhir, V, Summerscales, Tz, Sun, L, Sunil, S, Sur, A, Suresh, J, Sutton, Pj, Swinkels, Bl, Szczepanczyk, Mj, Tacca, M, Tait, Sc, Talbot, C, Tanner, Db, Tao, D, Tapai, M, Tapia, A, Tasson, Jd, Taylor, R, Tenorio, R, Terkowski, L, Thomas, M, Thomas, P, Thondapu, Sr, Thorne, Ka, Thrane, E, Tiwari, S, Tiwari, V, Toland, K, Tonelli, M, Tornasi, Z, Torres-Forne, A, Torrie, Ci, Toyra, D, Travasso, F, Traylor, G, Tringali, Mc, Tripathee, A, Trovato, A, Trozzo, L, Tsang, Kw, Tse, M, Tso, R, Tsukada, L, Tsuna, D, Tsutsui, T, Tuyenbayev, D, Ueno, K, Ugolini, D, Unnikrishnan, C, Urban, Al, Usman, Sa, Vahlbruch, H, Vajente, G, Valdes, G, Valentini, M, van Bakel, N, van Beuzekom, M, van den Brand, Jfj, Van Den Broeck, C, Vander-Hyde, Dc, van der Schaaf, L, Vanheijningen, Jv, van Veggel, Aa, Vardaro, M, Varma, V, Vass, S, Vasuth, M, Vecchio, A, Vedovato, G, Veitch, J, Veitch, Pj, Venkateswara, K, Venugopalan, G, Verkindt, D, Vetrano, F, Vicere, A, Viets, Ad, Vinciguerra, S, Vine, Dj, Vinet, Jy, Vitale, S, Vo, T, Vocca, H, Vorvick, C, Vyatchanin, Sp, Wade, Ar, Wade, Le, Wade, M, Walet, R, Walker, M, Wallace, L, Walsh, S, Wang, H, Wang, Jz, Wang, S, Wang, Wh, Wang, Yf, Ward, Rl, Warden, Za, Warner, J, Was, M, Watchi, J, Weaver, B, Wei, Lw, Weinert, M, Weinstein, Aj, Weiss, R, Wellmann, F, Wen, L, Wessel, K, Wessels, P, Westhouse, Jw, Wette, K, Whelan, Jt, Whiting, Bf, Whittle, C, Wilken, Dm, Williams, D, Williamson, Ar, Willis, Jl, Willke, B, Winkler, W, Wipf, Cc, Wittel, H, Woan, G, Woehler, J, Wofford, Jk, Wright, Jl, Wu, D, Wysocki, Dm, Xiao, S, Xu, R, Yamamoto, H, Yancey, Cc, Yang, L, Yang, Y, Yang, Z, Yap, Mj, Yazback, M, Yeeles, Dw, Yu, H, Yu, Hc, Yuen, Shr, Zadrozny, Ak, Zadrozny, A, Zanolin, M, Zelenova, T, Zendri, Jp, Zevin, M, Zhang, J, Zhang, L, Zhang, T, Zhao, C, Zhao, G, Zhou, M, Zhou, Z, Zhu, Xj, Zimmerman, Ab, Zucker, Me, Zweizig, J, (Astro)-Particles Physics, Arzoumanian, Z, Bogdanov, S, Cognard, I, Corongiu, A, Enoto, T, Freire, P, Gendreau, Kc, Guillemot, L, Harding, Ak, Jankowski, F, Keith, Mj, Kerr, M, Lyne, A, Palfreyman, J, Possenti, A, Ridolfi, A, Stappers, B, Theureau, G, Weltervrede, P, Université de Lyon-Université de Lyon-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3), Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, Centre National de la Recherche Scientifique (CNRS)-Institut National de Physique Nucléaire et de Physique des Particules du CNRS (IN2P3)-Université Paris-Sud - Paris 11 (UP11), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire des Sciences de l'Univers en région Centre (OSUC), Université Paris sciences et lettres (PSL)-Université d'Orléans (UO)-Centre National de la Recherche Scientifique (CNRS)-Université d'Orléans (UO), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)

Subjects
Known Pulsars, 010504 meteorology & atmospheric sciences, Astronomy, Astrophysics, Table (information), Vela, gravitational waves, pulsars, 01 natural sciences, Pulsar, 0103 physical sciences, Limit (mathematics), 010303 astronomy & astrophysics, gravitational wave, ComputingMilieux_MISCELLANEOUS, 0105 earth and related environmental sciences, Physics, [PHYS]Physics [physics], Gravitational wave, Two Harmonics, Astronomy and Astrophysics, Gravitational Waves, Known Pulsars, Two Harmonics, Erratum, LIGO, Amplitude, Space and Planetary Science, Erratum, Glitch (astronomy), [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph]
Abstract

Two analysis errors have been identified that affect the results for a handful of the high-value pulsars given in Table 1 of Abbott et al. (2019). One affects the Bayesian analysis for the five pulsars that glitched during the analysis period, and the other affects the 5n-vector analysis for J0711-6830. Updated results after correcting the errors are shown in Table 1, which now supersedes the results given for those pulsars in Table 1 of Abbott et al. (2019). Updated versions of figures can be seen in Figures 1-4. Bayesian analysis.-For the glitching pulsars, the signal phase evolution caused by the glitch was wrongly applied twice and was therefore not consistent with our expected model of the pulsar phase. This error did not affect the F/G-statistic or 5n-vector analysis. Analyses of the five pulsars PSR J0205+6449, PSR J0534+2200, PSR J0835-4510, PSR J1028-5819, and PSR J1718-3825 have been repeated after correcting for the error. There are small quantitative differences in the results, but the changes do not affect the main conclusions of the paper. The largest differences are for PSR J0835-4510 (the Vela pulsar), for which the updated upper limits from the Bayesian method are found to be between 1.1 and 2 times larger than those obtained when the error was present. This appears primarily to be due to the error leading to the decohering of a strong spectral line in the LIGO Livingston detector and thus lowering the amplitude limit. 5n-vector analysis.-An error was also identified in the settings of the 5n-vector analysis, which affected the upper limit computation at the rotation frequency for C21 95% of J0711-6830. Specifically, we found an incorrect choice for the range of amplitudes used to inject simulated signals in the O2 data. The updated upper limit is about 2.5 times worse than that obtained when the error was present. This error did not affect the Bayesian or F/G-statistic results. (Table Presented) (Figure Presented).

Published
2020
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36. Internal null controllability of the generalized Hirota-Satsuma system

Author

Nicolás Carreño, Eduardo Cerpa, Emmanuelle Crépeau, Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso), Univesidad Federico Santa-Maria, Valparaiso, Chile, Departamento de Matematica, Universidad Tecnica Federico Santa Maria, Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Equations aux Dérivées Partielles [2020-....] (EDP [2020-....]), Laboratoire Jean Kuntzmann [2020-....] (LJK [2020-....]), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2020-....] (UGA [2020-....])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....] (Grenoble INP [2020-....]), Université Grenoble Alpes [2020-....] (UGA [2020-....])-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-....]), Laboratoire de Mathématiques de Versailles (LMV), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Equations aux Dérivées Partielles [2016-2019] (EDP [2016-2019]), Laboratoire Jean Kuntzmann [2016-2019] (LJK [2016-2019]), and Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019] (Grenoble INP [2007-2019])-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])

Subjects
Inverse function theorem, 0209 industrial biotechnology, Control and Optimization, 010102 general mathematics, Linear system, Null (mathematics), Duality (optimization), 02 engineering and technology, Carleman estimates, 01 natural sciences, null controllability, Controllability, Computational Mathematics, Nonlinear system, 020901 industrial engineering & automation, Nonlinear Sciences::Exactly Solvable and Integrable Systems, Control and Systems Engineering, Bounded function, Korteweg-de Vries equation, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, [MATH]Mathematics [math], Korteweg–de Vries equation, Mathematics
Abstract

International audience; The generalized Hirota-Satsuma system consists of three coupled nonlinear Korteweg-de Vries (KdV) equations. By using two distributed controls it is proven in this paper that the local null controllability property holds when the system is posed on a bounded interval. First, the system is linearized around the origin obtaining two decoupled subsystems of third order dispersive equations. This linear system is controlled with two inputs, which is optimal. This is done with a duality approach and some appropriate Carleman estimates. Then, by means of an inverse function theorem, the local null controllability of the nonlinear system is proven.

Published
2020
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38. The fundamental group of a log terminal T-variety

Author

Laface, Antonio, Liendo, Alvaro, Moraga, Joaquín, Departamento de Matematicas, Universidad de Concepcion, Universidad de Concepción [Chile], Instituto de Matematica y Fisica, Universidad Talca, Department of Mathematics - University of Utah, University of Utah, and Comision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)Anillo ACT 1415 PIAComision Nacional de Investigacion Cientifica y Tecnologica (CONICYT)CONICYT FONDECYT11608641150732

Subjects
Fundamental groups, Torus actions, T-varieties, [MATH]Mathematics [math]
Abstract

International audience; We introduce an approach to study the fundamental group of a log terminal T-variety. As applications, we prove the simply connectedness of the spectrum of the Cox ring of a complex Fano variety, we compute the fundamental group of a rational log terminal T-variety of complexity one, and we study the local fundamental group of a log terminal T-singularity with a good torus action and trivial GIT decomposition.

Published
2019
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40. Contact exponent and the Milnor number of plane curve singularities

Author

Evelia Rosa Garcia Barroso, Arkadiusz Płoski, Krasiński, Tadeusz, Spodzieja, Stanisław, Departamento de Matematicas, Estadistica e I.O. Seccion de Matematicas, Universidad de La Laguna Apartado de Correos 456, and Department of Mathematics and Physics, Kielce University of Technology

Subjects
Mathematics::Algebraic Geometry
Abstract

We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is an equisingularity invariant and give a new proof of the stability of the maximal contact. Then we prove a bound for the Milnor number and determine the equisingularity class of algebroid curves for which this bound is attained. We do not use the method of Newton's diagrams. Our tool is the logarithmic distance developed in [GB-P1].

Published
2019

41. Controlling recirculation rate in minimal-time bioremediation of natural water resources

Author

Riquelme, Victor, Rapaport, Alain, Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso), Univesidad Federico Santa-Maria, Valparaiso, Chile, Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie (MISTEA), Institut National de la Recherche Agronomique (INRA)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro)-Institut National de la Recherche Agronomique (INRA), Rapaport, Alain, Universidad Tecnica Frederico Santa Maria, and Partenaires INRAE

Subjects
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; We revisit the minimal time problem of in-situ decontamination of large water resources with a bioreactor, considering a recirculation flow rate in the resource as an additional control. This new problem has two manipulated inputs : 1. the flow rate of the treatment in thebioreactor (which enters nonlinearly in the dynamics because of the biological dependancy between the flow rate and the concentration at the output of the bioreactor) 2. the flow rate of the recirculation in the resource between the pumping and reinjection locations (which enters linearly the dynamics). Although the velocity set of the dynamics is non convex, we show that the optimal control is reached amongnon-relaxed controls. The optimal strategy consists in three sequential steps: 1. do not recirculate water and take the flow rate of treatment that maximizes the concentration decay in the resource. 2. recirculate water at maximum rate and carry on with the flow rate that maximizesthe concentration decay. 3. carry on with recirculation but do not treat the water (i.e. bypass the bioreactor). Finally, we show on numericalsimulations that significant gains in processing time can be achieved when controlling the recirculation flow rate.

Published
2018

42. Technical specification IEC TS 62989:2018 – Primary optics for concentrator photovoltaic systems

Author

Sam Carter, César Domínguez, Hideto Kasai, Philippe Voarino, Jaione Bengoechea, David C. Miller, Ralf Leutz, Thorsten Hornung, Thomas Arndt, Rebeca Herrero, Peter Nitz, Marta Victoria, Steve Askins, René Kogler, Steve Scott, Evonik Industries AG [Darmstadt], Universidad Politécnica de Madrid (UPM), Centro Nacional de Energías Renovables - Fundación CENER-CIEMAT (CENER), RayGen Resources Pty Ltd [Blackburn], Departamento de Matematicas y Computacion (Department of Mathematics and Computer Science), Universidad de La Rioja (UR), Fraunhofer Institute for Solar Energy Systems (Fraunhofer ISE), Fraunhofer (Fraunhofer-Gesellschaft), Kuraray [Tokyo], leopil – Leutz Optics and Illumination UG [Munich], Proof search and reasoning with logic specifications (PARSIFAL), Laboratoire d'informatique de l'École polytechnique [Palaiseau] (LIX), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Orafol Americas, Inc [Avon], Département des Technologies Solaires (DTS), Laboratoire d'Innovation pour les Technologies des Energies Nouvelles et les nanomatériaux (LITEN), Institut National de L'Energie Solaire (INES), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut National de L'Energie Solaire (INES), Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Institut National de L'Energie Solaire (INES), and Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Measure (data warehouse), business.industry, Computer science, Energía Eléctrica, 020206 networking & telecommunications, 02 engineering and technology, Química, 021001 nanoscience & nanotechnology, Visual appearance, Encircled energy, [SPI]Engineering Sciences [physics], Optics, Documentation, 0202 electrical engineering, electronic engineering, information engineering, Key (cryptography), Round robin test, Concentrator photovoltaic, 0210 nano-technology, business, Product identification
Abstract

The first edition of the Technical Specification (TS) on Primary Optics for Concentrator Photovoltaic (CPV) Systems, IEC TS 62989:2018, has been published by the International Electrotechnical Commission (IEC), on March 8th, 2018. TS 62989 covers aspects related to the primary optics including: product identification, optical characteristics, mechanical characteristics, materials, (design) geometry, and visual appearance. This paper focuses on the key aspects of the norm, including optical performance, in order to promote the awareness and use of the standard. We describe the three methods intended to measure the key optical characteristics of the primary elements, i.e. focal spot size and optical efficiency, by using the encircled energy. The three methods are using different light sources, optical components and receiver sensors, but yielded very similar results in a round robin test. This justifies the continued use of all three methods. The use of a website (opticstests.pbworks.com) for documentation of discussions and references was novel to the standard development. The website proved to be useful for the introduction of new members of the group. The website helped to keep track of changes to the document as well as the required actions of the project team.The first edition of the Technical Specification (TS) on Primary Optics for Concentrator Photovoltaic (CPV) Systems, IEC TS 62989:2018, has been published by the International Electrotechnical Commission (IEC), on March 8th, 2018. TS 62989 covers aspects related to the primary optics including: product identification, optical characteristics, mechanical characteristics, materials, (design) geometry, and visual appearance. This paper focuses on the key aspects of the norm, including optical performance, in order to promote the awareness and use of the standard. We describe the three methods intended to measure the key optical characteristics of the primary elements, i.e. focal spot size and optical efficiency, by using the encircled energy. The three methods are using different light sources, optical components and receiver sensors, but yielded very similar results in a round robin test. This justifies the continued use of all three methods. The use of a website (opticstests.pbworks.com) for documentation ...

Published
2018
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43. Twisted calculus

Author

Bernard Le Stum, Adolfo Quiros Gracian, Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Departamento de Matematicas [Madrid], Universidad Autónoma de Madrid (UAM), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Universidad Autonoma de Madrid (UAM), Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Departamento de Matemáticas, and Universidad Autonoma de Madrid ( UAM )

Subjects
Mathematics - Algebraic Geometry, Algebra and Number Theory, 010102 general mathematics, 0103 physical sciences, FOS: Mathematics, 010307 mathematical physics, [MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG], 0101 mathematics, 01 natural sciences, Algebraic Geometry (math.AG), [ MATH.MATH-AG ] Mathematics [math]/Algebraic Geometry [math.AG]
Abstract

International audience; A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. We study them and show that, under some general hypothesis, the categories of twisted modules and integrable twisted differential modules are equivalent. As particular cases, one recovers classical results from the theory of finite difference equations or q-difference equations.

Published
2018
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44. Controllability and Positivity Constraints in Population Dynamics with Age Structuring and Diffusion

Author

Enrique Zuazua, Debayan Maity, Marius Tucsnak, 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), Departamento de Matematicas [Madrid], Universidad Autonoma de Madrid (UAM), Deusto Institute of Technology (DeustoTech), University of Deusto, Universidad de Deusto (DEUSTO), and UAM. Departamento de Matemáticas

Subjects
0209 industrial biotechnology, Population dynamics, Matemáticas, General Mathematics, Population, AMS subject classifications 93B03 ,93B05, 92D25, 02 engineering and technology, Interval (mathematics), 01 natural sciences, 020901 industrial engineering & automation, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Observability, 0101 mathematics, education, Mathematics, education.field_of_study, Null controllability, Semigroup, Applied Mathematics, 010102 general mathematics, Linear system, State (functional analysis), Controllability, Controllability with positivity constraints, Variable (computer science), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

This Accepted Manuscript will be available for reuse under a CC BY-NC-ND licence after 24 months of embargo period, In this article, we study the null controllability of a linear system coming from a population dynamics model with age structuring and spatial diffusion (of Lotka–McKendrick type). The control is localized in the space variable as well as with respect to the age. The first novelty we bring in is that the age interval in which the control needs to be active can be arbitrarily small and does not need to contain a neighbourhood of 0. The second one is that we prove that the whole population can be steered into zero in a uniform time, without, as in the existing literature, excluding some interval of low ages. Moreover, we improve the existing estimates of the controllability time and we show that our estimates are sharp, at least when the control is active for very low ages. Finally, we show that the system can be steered between two positive steady states by controls preserving the positivity of the state trajectory. The method of proof, combining final-state observability estimates with the use of characteristics and with L∞ estimates of the associated semigroup, avoids the explicit use of parabolic Carleman estimates, The research of Enrique Zuazua was supported by the Advanced Grant DyCon (Dynamical Control) of the European Research Council Executive Agency (ERC), the MTM2014-52347 and MTM2017-92996 Grants of the MINECO (Spain) and the ICON project of the French ANR-16-ACHN-0014

Published
2018
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45. Optimal Population Control Through Sterile Males

Author

Trélat, Emmanuel, Zhu, Jiamin, Zuazua, Enrique, Control And GEometry (CaGE ), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-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), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Fundación Deusto, Departamento de Matematicas [Madrid], Universidad Autonoma de Madrid (UAM), and Universidad Autónoma de Madrid (UAM)

Subjects
[SDV.EE]Life Sciences [q-bio]/Ecology, environment, fungi, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

In this article, we propose a new model for describing the population evolution while considering the effect of the sterile insect release method (SIRM) and the Allee effect. Different from classical deterministic or stochastic modelings, our model is developed as a hydrodynamic limit of an interacting particle system. Some system solutions are then studied and an optimal control problem is formulated in order to design control strategies for eradicating the target pest population with as less sterile males as possible. Numerical results show that the population eradicating mission can be achieved when sufficiently large sterile male release rate is provided, and that the Allee effect can help to reduce the use of sterile males.

Published
2017

46. Free algebraic structures on the permutohedra

Author

Pierre-Louis Curien, Emily Burgunder, Maria Ronco, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Preuves, Programmes et Systèmes (PPS), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matematicas, Universidad de Valparaiso [Chile], Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pure mathematics, Algebraic structure, Coalgebra, Structure (category theory), Polytope, 02 engineering and technology, 01 natural sciences, Mathematics::Algebraic Topology, Bialgebra, Mathematics::K-Theory and Homology, Mathematics::Category Theory, Mathematics::Quantum Algebra, FOS: Mathematics, 0202 electrical engineering, electronic engineering, information engineering, Mathematics - Combinatorics, 0101 mathematics, [MATH]Mathematics [math], ComputingMilieux_MISCELLANEOUS, Mathematics, Algebra and Number Theory, 010102 general mathematics, Mathematics::Rings and Algebras, Order (ring theory), Basis (universal algebra), Mathematics - Rings and Algebras, Rings and Algebras (math.RA), 020201 artificial intelligence & image processing, Combinatorics (math.CO), Primary 16T30, Secondary: 05E05, Vector space
Abstract

Tridendriform algebras are a type of associative algebras, introduced independently by F. Chapoton and by J.-L. Loday and the third author, in order to describe operads related to the Stasheff polytopes. The vector space $\st$ spanned by the faces of permutohedra has a natural structure of tridendriform bialgebra, we prove that it is free as a tridendriform algebra and exhibit a basis. Our result implies that the subspace of primitive elements of the coalgebra $\st$ , equipped with the coboundary map of permutohedra, is a free cacti algebra., 35 pages

Published
2017

47. Cooperative Vision-Based Object Transportation by Two Humanoid Robots in a Cluttered Environment

Author

Wael Suleiman, Jean-Bernard Hayet, Claudia Esteves, Antoine Rioux, Université de Sherbrooke (UdeS), Departamento de Matematicas, Departemento de Matematicas, Universidad de Guanajato-Universidad de Guanajato, Centro de Investigación en Matemáticas (CIMAT), and Consejo Nacional de Ciencia y Tecnología [Mexico] (CONACYT)

Subjects
Scheme (programming language), 0209 industrial biotechnology, Computer science, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Odometry, Artificial Intelligence, 0202 electrical engineering, electronic engineering, information engineering, Collaborative tasks, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Computer vision, Motion planning, Projection (set theory), computer.programming_language, business.industry, Whole-body control, Mechanical Engineering, Object (computer science), Navigation, SLAM, Trajectory, Robot, 020201 artificial intelligence & image processing, Artificial intelligence, business, computer, Humanoid robot
Abstract

International audience; Although in recent years there have been quite a few studies aimed at the navigation of robots in cluttered environments, few of these have addressed the problem of robots navigating while moving a large or heavy object. Such a functionality is especially useful when transporting objects of different shapes and weights without having to modify the robot hardware. In this work, we tackle the problem of making two humanoid robots navigate in a cluttered environment while transporting a very large object that simply could not be moved by a single robot. We present a complete navigation scheme, from the incremental construction of a map of the environment and the computation of collision-free trajec-tories to the design of the control to execute those trajectories. We present experiments made on real Nao robots, equipped with RGB-D sensors mounted on their heads, moving an object around obstacles. Our experiments show that a significantly large object can be transported without modifying the robot main hardware, and therefore that our scheme enhances the humanoid robots capacities in real-life situations. Our contributions are: (1) a low-dimension multi-robot motion planning algorithm that finds an obstacle-free trajectory, by using the constructed map of the environment as an input, (2) a framework that produces continuous and consistent odometry data, by fusing the visual and the robot odometry information, (3) a synchronization system that Two Nao robots holding an object together. We propose a motion planning strategy for the Nao-object-Nao system to navigate in a cluttered environment and a synchronization approach that allows the motions done by the two Naos without compromising the whole system stability because of the robots swinging movement. uses the projection of the robots based on their hands positions coupled with the visual feedback error computed from a frontal camera, (4) an efficient real-time whole-body control scheme that controls the motions of the closed-loop robot-object-robot system.

Published
2017
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48. Semi-Group Theory for the Stokes Operator with Navier-Type Boundary Conditions on L p -Spaces

Author

Hind Al Baba, Miguel Escobedo, Chérif Amrouche, Laboratoire de Mathématiques et de leurs Applications [Pau] (LMAP), Université de Pau et des Pays de l'Adour (UPPA)-Centre National de la Recherche Scientifique (CNRS), Departamento de Matematicas, and Universidad del Pais Vasco / Euskal Herriko Unibertsitatea [Espagne] (UPV/EHU)

Subjects
Mathematics::Analysis of PDEs, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Type (model theory), [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA], 01 natural sciences, Omega, Physics::Fluid Dynamics, symbols.namesake, Mathematics (miscellaneous), Simply connected space, Stokes parameters, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, [MATH]Mathematics [math], Stokes operator, Mathematics, Mechanical Engineering, 010102 general mathematics, Mathematical analysis, 010101 applied mathematics, Kernel (algebra), [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG], symbols, Analysis, Group theory, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

In this article we consider the Stokes problem with Navier-type boundary conditions on a domain $${\Omega}$$ , not necessarily simply connected. Since, under these conditions, the Stokes problem has a non trivial kernel, we also study the solutions lying in the orthogonal of that kernel. We prove the analyticity of several semigroups generated by the Stokes operator considered in different functional spaces. We obtain strong, weak and very weak solutions for the time dependent Stokes problem with the Navier-type boundary condition under different hypotheses on the initial data u 0 and external force f. Then, we study the fractional and pure imaginary powers of several operators related with our Stokes operators. Using the fractional powers, we prove maximal regularity results for the homogeneous Stokes problem. On the other hand, using the boundedness of the pure imaginary powers, we deduce maximal $${L^{p}-L^{q}}$$ regularity for the inhomogeneous Stokes problem.

Published
2017
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49. The Mayer and Minimum Time Problems with Stratified State Constraints *

Author

Peter R. Wolenski, Cristopher Hermosilla, Hasnaa Zidani, Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso), Univesidad Federico Santa-Maria, Valparaiso, Chile, Department of Mathematics [Baton Rouge] (LSU Mathematics), Louisiana State University (LSU), Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), ANR-12-BS01-0008,HJnet,Equations de Hamilton-Jacobi sur des structures hétérogènes et des réseaux(2012), and European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011)

Subjects
Statistics and Probability, 0209 industrial biotechnology, Mathematical optimization, State constraints, stratified structure, Constraint domain, 02 engineering and technology, 01 natural sciences, 020901 industrial engineering & automation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, Mathematics, Numerical Analysis, Applied Mathematics, 010102 general mathematics, Minimum time, minimal time function, Optimal control, Controllability, Geometry and Topology, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Hamilton-Jacobi equations, Mayer problem, Analysis, Hamiltonian (control theory)
Abstract

International audience; This paper studies optimal control problems with state constraints by imposing structural assumptions on the constraint domain coupled with a tangential restriction with the dynamics. These assumptions replace pointing or controllability assumptions that are common in the literature, and provide a framework under which feasible boundary trajectories can be analyzed directly. The value functions associated with the state constrained Mayer and minimal time problems are characterized as solutions to a pair of Hamilton-Jacobi inequalities with appropriate boundary conditions. The novel feature of these inequalities lies in the choice of the Hamiltonian.

Published
2017
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50. Hamilton-Jacobi-Bellman equations for optimal control processes with convex state constraints

Author

Hermosilla, Cristopher, Vinter, Richard, Zidani, Hasnaa, Departamento de Matematicas, Univesidad Tecnica Federico Santa-Maria (Valparaiso), Univesidad Federico Santa-Maria, Valparaiso, Chile, Department of Electrical and Electronic Engineering [London] (DEEE), Imperial College London, Optimisation et commande (OC), Unité de Mathématiques Appliquées (UMA), École Nationale Supérieure de Techniques Avancées (ENSTA Paris)-École Nationale Supérieure de Techniques Avancées (ENSTA Paris), European Project: 264735,EC:FP7:PEOPLE,FP7-PEOPLE-2010-ITN,SADCO(2011), Zidani, Hasnaa, and Sensitivity Analysis for Deterministic Controller Design - SADCO - - EC:FP7:PEOPLE2011-01-01 - 2014-12-31 - 264735 - VALID

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience

Published
2017

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