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504 results on '"Legendre, Guillaume"'

4. A simple flattening lower bound for solutions to some linear integrodifferential equations

Author

Bouin, Emeric, Coville, Jérôme, and Legendre, Guillaume

Subjects
Mathematics - Analysis of PDEs
Abstract

Estimates on the asymptotic behaviour of solution to linear integro-differential equations are fundamental in understanding the dynamics occuring in many nonlocal evolution problems. They are usually derived by using precise decay estimates on the heat kernel of the considered diffusion process. In this note, we show that for some generic jump diffusion and particular initial data, one can derive a lower bound of the asymptotic behaviour of the solution using a simple PDE argument. This is viewed as an independant preliminary brick to study invasion phenomena in nonlinear reaction diffusion problems.

Published
2023

6. On the method of reflections

Author

Laurent, Philippe, Legendre, Guillaume, and Salomon, Julien

Subjects
Mathematics - Analysis of PDEs
Abstract

This paper aims at reviewing and analysing the method of reflections. The latter is an iterative procedure designed to linear boundary value problems set in multiply connected domains. Being based on a decomposition of the domain boundary, this method is particularly well-suited to numerical solvers relying on integral representation formulas. For the parallel and sequential forms of the method appearing in the literature, we propose a general abstract formulation in a given Hilbert setting and interpret the procedure in terms of subspace corrections. We then prove the unconditional convergence of the sequential form and propose a modification of the parallel one that makes it unconditionally converging. An alternative proof of convergence is provided in a case which does not fit into the previous framework. We finally present some numerical tests.

Published
2021

7. Acceleration in integro-differential combustion equations

Author

Bouin, Emeric, Coville, Jérôme, and Legendre, Guillaume

Subjects
Mathematics - Analysis of PDEs
Abstract

We study acceleration phenomena in monostable integro-differential equations with ignition nonlinearity. Our results cover fractional Laplace operators and standard convolutions in a unified way, which is also a contribution of this paper. To achieve this, we construct a sub-solution that captures the expected dynamics of the accelerating solution, and this is here the main difficulty. This study involves the flattening effect occurring in accelerated propagation phenomena., Comment: Version 0. Changes to come. arXiv admin note: substantial text overlap with arXiv:2105.09911

Published
2021

8. Sharp exponent of acceleration in general nonlocal equations with a weak Allee effect

Author

Bouin, Emeric, Coville, Jérôme, and Legendre, Guillaume

Subjects
Mathematics - Analysis of PDEs
Abstract

We study an acceleration phenomenon arising in monostable integro-differential equations with a weak Allee effect. Previous works have shown its occurrence and have given correct upper bounds on the rate of expansion in some particular cases, but precise lower bounds were still missing. In this paper, we provide a sharp lower bound for this acceleration rate, valid for a large class of dispersion operators. Our results manage to cover fractional Laplace operators and standard convolutions in a unified way, which is new in the literature. A first very important result of the paper is a general flattening estimate of independent interest: this phenomenon appears regularly in acceleration situations, but getting quantitative estimates is most of the time open. This estimate at hand, we construct a very subtle sub-solution that captures the expected dynamics of the accelerating solution (rates of expansion and flattening) and identifies several various regimes that appear in the dynamics depending on the parameters of the problem.

Published
2021

10. Convergence analysis of adaptive DIIS algorithms with application to electronic ground state calculations

Author

Chupin, Maxime, Dupuy, Mi-Song, Legendre, Guillaume, and Séré, Eric

Subjects
Mathematics - Numerical Analysis
Abstract

This paper deals with a general class of algorithms for the solution of fixed-point problems that we refer to as \emph{Anderson--Pulay acceleration}. This family includes the DIIS technique and its variant sometimes called commutator-DIIS, both introduced by Pulay in the 1980s to accelerate the convergence of self-consistent field procedures in quantum chemistry, as well as the related Anderson acceleration which dates back to the 1960s, and the wealth of techniques they have inspired. Such methods aim at accelerating the convergence of any fixed-point iteration method by combining several iterates in order to generate the next one at each step. This extrapolation process is characterised by its \emph{depth}, i.e. the number of previous iterates stored, which is a crucial parameter for the efficiency of the method. It is generally fixed to an empirical value. In the present work, we consider two parameter-driven mechanisms to let the depth vary along the iterations. In the first one, the depth grows until a certain nondegeneracy condition is no longer satisfied; then the stored iterates (save for the last one) are discarded and the method "restarts". In the second one, we adapt the depth continuously by eliminating at each step some of the oldest, less relevant, iterates. In an abstract and general setting, we prove under natural assumptions the local convergence and acceleration of these two adaptive Anderson--Pulay methods, and we show that one can theoretically achieve a superlinear convergence rate with each of them. We then investigate their behaviour in quantum chemistry calculations. These numerical experiments show that both adaptive variants exhibit a faster convergence than a standard fixed-depth scheme, and require on average less computational effort per iteration. This study is complemented by a review of known facts on the DIIS, in particular its link with the Anderson acceleration and some multisecant-type quasi-Newton methods., Comment: Final version to appear in ESAIM:M2AN

Published
2020

11. Evolution of anisotropic diffusion in two-dimensional heterogeneous environments

Author

Bouin, Emeric, Legendre, Guillaume, Lou, Yuan, and Slover, Nichole

Subjects
Mathematics - Analysis of PDEs, Quantitative Biology - Populations and Evolution
Abstract

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these probabilities as dispersal strategies. We show that the evolutionarily stable strategies are to move in one direction only. Our results predict that it is more beneficial for the species to choose the direction with smaller variation in the resource distribution. This finding seems to be in agreement with the classical results of Hasting [15] and Dockery et al. [11] for the evolution of slow dispersal, i.e. random diffusion is selected against in spatially heterogeneous environments. These conclusions also suggest that broader dispersal strategies should be considered regarding the movement in heterogeneous habitats.

Published
2020

12. Pelvic exam in Gynecology and Obstetrics: French Guidelines for Clinical Practice

Author

Deffieux, Xavier, Pizzoferrato, Anne-Cécile, Gaucher, Laurent, Rousset-Jablonski, Christine, Le Ray, Camille, Brillac, Thierry, Maruani, Julia, Maitrot-Mantelet, Lorraine, Mignot, Stéphanie, Athiel, Yoann, Baffet, Hortense, Bailleul, Alexandre, Bernard, Valérie, Bourdon, Mathilde, Cardaillac, Claire, Carneiro, Yaritza, Chariot, Patrick, Corroenne, Romain, Dabi, Yohann, Dahlem, Laurence, Frank, Sophie, Freyens, Anne, Grouthier, Virginie, Hernandez, Isabelle, Iraola, Elisabeth, Lambert, Marie, Lauchet, Nadege, Legendre, Guillaume, Le Lous, Maela, Louis-Vahdat, Christine, Martinat Sainte-Beuve, Anne, Masson, Marine, Matteo, Caroline, Pinton, Anne, Sabbagh, Emmanuelle, Sallee, Camille, Thubert, Thibault, Heron, Isabelle, Artzner, France, Tavenet, Arounie, Gantois, Adrien, and Fauconnier, Arnaud

Published
2023
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13. Tranexamic acid for reduction of blood loss after Caesarean delivery: a cost-effectiveness analysis of the TRAAP2 trial

Author

Senat, Marie-Victoire, Le Lous, Maëla, Winer, Norbert, Rozenberg, Patrick, Kayem, Gilles, Verspyck, Eric, Fuchs, Florent, Azria, Elie, Gallot, Denis, Korb, Diane, Desbrière, Raoul, Le Ray, Camille, Chauleur, Céline, de Marcillac, Fanny, Perrotin, Franck, Parant, Olivier, Salomon, Laurent J., Gauchotte, Emilie, Bretelle, Florence, Sananès, Nicolas, Bohec, Caroline, Mottet, Nicolas, Legendre, Guillaume, Letouzey, Vincent, Haddad, Bassam, Vardon, Delphine, Madar, Hugo, Froeliger, Alizée, Daniel, Valérie, Pharm.D, Regueme, Sophie, Roussillon, Caroline, Darsonval, Astrid, Sentilhes, Loïc, Bénard, Antoine, Petit, Solène, and Deneux-Tharaux, Catherine

Published
2023
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14. Examen pelvien en gynécologie et obstétrique : recommandations pour la pratique clinique

Author

Deffieux, Xavier, Rousset-Jablonski, Christine, Gantois, Adrien, Brillac, Thierry, Maruani, Julia, Maitrot-Mantelet, Lorraine, Mignot, Stéphanie, Gaucher, Laurent, Athiel, Yoann, Baffet, Hortense, Bailleul, Alexandre, Bernard, Valérie, Bourdon, Mathilde, Cardaillac, Claire, Carneiro, Yaritza, Chariot, Patrick, Corroenne, Romain, Dabi, Yohann, Dahlem, Laurence, Frank, Sophie, Freyens, Anne, Grouthier, Virginie, Hernandez, Isabelle, Iraola, Elisabeth, Lambert, Marie, Lauchet, Nadege, Legendre, Guillaume, Le Lous, Maela, Louis-Vahdat, Christine, Martinat Sainte-Beuve, Anne, Masson, Marine, Matteo, Caroline, Pinton, Anne, Sabbagh, Emmanuelle, Sallee, Camille, Thubert, Thibault, Heron, Isabelle, Pizzoferrato, Anne-Cécile, Artzner, France, Tavenet, Arounie, Le Ray, Camille, and Fauconnier, Arnaud

Published
2023
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16. Posttraumatic stress disorder 2 months after cesarean delivery: a multicenter prospective study

Author

Sentilhes, Loïc, Senat, Marie V., Le Lous, Maëla, Winer, Norbert, Rozenberg, Patrick, Kayem, Gilles, Verspyck, Eric, Fuchs, Florent, Azria, Elie, Gallot, Denis, Korb, Diane, Desbrière, Raoul, Le Ray, Camille, Chauleur, Céline, de Marcillac, Fanny, Perrotin, Franck, Parant, Olivier, Salomon, Laurent J., Gauchotte, Emilie, Bretelle, Florence, Sananès, Nicolas, Bohec, Caroline, Mottet, Nicolas, Legendre, Guillaume, Letouzey, Vincent, Haddad, Bassam, Vardon, Delphine, Madar, Hugo, Mattuizzi, Aurélien, Froeliger, Alizée, Daniel, Valérie, Regueme, Sophie, Roussillon, Caroline, Bénard, Antoine, Georget, Aurore, Darsonval, Astrid, Deneux-Tharaux, Catherine, and Loussert, Lola

Published
2024
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30. Posttraumatic stress disorder 2 months after cesarean delivery: a multicenter prospective study

Author

Froeliger, Alizée, primary, Deneux-Tharaux, Catherine, additional, Loussert, Lola, additional, Madar, Hugo, additional, Sentilhes, Loïc, additional, Senat, Marie V., additional, Le Lous, Maëla, additional, Winer, Norbert, additional, Rozenberg, Patrick, additional, Kayem, Gilles, additional, Verspyck, Eric, additional, Fuchs, Florent, additional, Azria, Elie, additional, Gallot, Denis, additional, Korb, Diane, additional, Desbrière, Raoul, additional, Le Ray, Camille, additional, Chauleur, Céline, additional, de Marcillac, Fanny, additional, Perrotin, Franck, additional, Parant, Olivier, additional, Salomon, Laurent J., additional, Gauchotte, Emilie, additional, Bretelle, Florence, additional, Sananès, Nicolas, additional, Bohec, Caroline, additional, Mottet, Nicolas, additional, Legendre, Guillaume, additional, Letouzey, Vincent, additional, Haddad, Bassam, additional, Vardon, Delphine, additional, Mattuizzi, Aurélien, additional, Froeliger, Alizée, additional, Daniel, Valérie, additional, Regueme, Sophie, additional, Roussillon, Caroline, additional, Bénard, Antoine, additional, Georget, Aurore, additional, and Darsonval, Astrid, additional

Published
2024
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31. Advanced Insights into Human Uterine Innervation: Implications for Endometriosis and Pelvic Pain

Author

Astruc, Audrey, primary, Roux, Léa, additional, Robin, Fabien, additional, Sall, Ndeye Racky, additional, Dion, Ludivine, additional, Lavoué, Vincent, additional, Legendre, Guillaume, additional, Leveque, Jean, additional, Bessede, Thomas, additional, Bertrand, Martin, additional, Odimba Mpoy, Jules, additional, Nzau-Ngoma, Emmanuel, additional, Morandi, Xavier, additional, Chedotal, Alain, additional, Le Lous, Maela, additional, and Nyangoh Timoh, Krystel, additional

Published
2024
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37. The impact of the COVID-19 coronavirus pandemic on the surgical management of gynecological cancers: Analysis of the multicenter database of the French SCGP and the FRANCOGYN group

Author

Jouen, Théo, Gauthier, Tristan, Azais, Henri, Bendifallah, Sofiane, Chauvet, Pauline, Fernandez, Herve, Kerbage, Yohan, Lavoue, Vincent, Lecointre, Lise, Mimoun, Camille, Ouldamer, Lobna, Seidler, Stéphanie, Siffert, Marc, Vallin, Anne-Lyse, Spiers, Andrew, Descamps, Philippe, Lacorre, Aymeline, and Legendre, Guillaume

Published
2021
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42. Concentration Phenomenon in Some Non-Local Equation

Author

Bonnefon, Olivier, Coville, Jérôme, and Legendre, Guillaume

Subjects
Mathematics - Analysis of PDEs
Abstract

We are interested in the long time behaviour of the positive solutions of the Cauchy problem involving the following integro-differential equation $$\partial\_t u(t, x) = \left(a(x) -- \int\_{\Omega} k(x, y)u(t, y) dy\right ) u(t, x) + \int\_{\Omega} m(x, y)[u(t, y) -- u(t, x)] dy\quad \text{ for}\quad (t, x) $\in$ \mathbb{R}\_{+} \times \Omega,$$ together with the initial condition $u(0, \cdot) = u0 \quad \text{ in }\quad \Omega$. Such a problem is used in population dynamics models to capture the evolution of a clonal population structured with respect to a phenotypic trait. In this context, the function u represents the density of individuals characterized by the trait, the domain of trait values $\Omega$ is a bounded subset of $\mathbb{R}^N$ , the kernels $k$ and $m$ respectively account for the competition between individuals and the mutations occurring in every generation, and the function a represents a growth rate. When the competition is independent of the trait, we construct a positive stationary solution which belongs to the space of Radon measures on $\Omega$. Moreover, when this '' stationary '' measure is regular and bounded, we prove its uniqueness and show that, for any non negative initial datum in $L^{\infty} (\Omega) \cap L^1 (\Omega)$, the solution of the Cauchy problem converges to this limit measure in $L^2 (\Omega)$. We also construct an example for which the measure is singular and non-unique, and investigate numerically the long time behaviour of the solution in such a situation. These numerical simulations seem to reveal some dependence of the limit measure with respect to the initial datum.

Published
2015

44. Interstitial pregnancy management: A multicentric analysis of 98 patients from the FRANCOGENT group comparing surgery and medical treatment

Author

Dabreteau, Thomas, primary, Puchar, Anne, additional, Timoh, Krystel Nyangoh, additional, Fauconnier, Arnaud, additional, Legendre, Guillaume, additional, Touboul, Cyril, additional, Lavoué, Vincent, additional, Thubert, Thibault, additional, Lecarpentier, Edouard, additional, Haddad, Bassam, additional, and Dabi, Yohann, additional

Published
2023
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