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X-WR-CALDESC:Évènements pour Laboratoire de Mathématiques de Versailles
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DTSTART;TZID=Europe/Paris:20250213T140000
DTEND;TZID=Europe/Paris:20250213T150000
DTSTAMP:20260419T192719
CREATED:20241209T100852Z
LAST-MODIFIED:20250214T125158Z
UID:13456-1739455200-1739458800@lmv.math.cnrs.fr
SUMMARY:EDP : Annabelle Collin (Université de Nantes) : Sequential Data Assimilation for Oncology: Theory & Practice illustrations.
DESCRIPTION:Abstract: The development of PDE models capable of describing tumor growth may help to monitor disease progression or predict the efficacy of different therapeutic strategies. However\, to be truly informative or predictive\, these models need to be corrected and/or parameterized with available observations. The aim of this talk is to present some sequential data assimilation strategies that address these types of problems. A first\, rather simple example will be presented to introduce the concepts\, followed by two parts. More specifically\, in the first part\, we focus on a Luenberger observer that can handle 3D tumor front data. In the second part\, we focus on the combination of a Luenberger observer with a population-based Kalman observer\, which allows the use of repeated measurements in configurations with common priors (e.g.\, multiple subjects in a clinical trial or repeated biological measurements) when data are sparse or corrupted by noise. Theoretical results and numerical illustrations with synthetic and real data are presented for both parts.
URL:https://lmv.math.cnrs.fr/evenenement/edp-annabelle-collin-universite-de-nantes/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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DTSTART;TZID=Europe/Paris:20250213T153000
DTEND;TZID=Europe/Paris:20250213T163000
DTSTAMP:20260419T192719
CREATED:20241209T101000Z
LAST-MODIFIED:20250214T125204Z
UID:13458-1739460600-1739464200@lmv.math.cnrs.fr
SUMMARY:EDP : Simão Correia (Instituto Superior Técnico\, Lisbonne) : Blow-up stability of self-similar solutions to the modified Korteweg-de Vries equation
DESCRIPTION:Abstract : Self-similar solutions for the modified Korteweg-de Vries equation are of both physical and mathematical interest. On the physical side\, among several applications\, they model the formation of sharp corners in planar vortex patches. Mathematically\, they describe the asymptotic behavior of solutions for large times and present a blow-up behavior at the initial time. Due to their scaling invariance\, these solutions display several critical features (time decay\, spatial decay and regularity)\, which means that the existing theory is not applicable. In this talk\, I will show that the blow-up structure is stable under subcritical perturbations of any size. The proof relies on new a priori estimates for the modified KdV at critical regularity and on an infinite normal form reduction. This is joint work with R. Côte.
URL:https://lmv.math.cnrs.fr/evenenement/edp-simao-correia-instituto-superior-tecnico-lisbonne/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire EDP
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