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Euclid preparation. Review of forecast constraints on dark energy and modified gravity
No full textInternational audienceThe Euclid mission has been designed to provide, as one of its main deliverables, information on the nature of the gravitational interaction, which determines the expansion of the Universe and the formation of structures. Thus, Euclid has the potential to test deviations from general relativity that will allow us to shed light on long-lasting problems in the standard cosmological model, CDM. Euclid will mainly do this by using two complementary probes: weak gravitational lensing and galaxy clustering. In this paper we review pre-launch Euclid analyses for dark energy and modified gravity. These include forecast constraints with future Euclid data on cosmological parameters for different cosmological models, such as a time-varying dark energy component, phenomenological modifications of the perturbation sector and specific modified gravity models, with further extensions that include neutrino physics and the coupling to the electromagnetic sector through the fine-structure constant. We review the study of the impact of nonlinear clustering methods on beyond-CDM constraints with Euclid. This is of fundamental importance to efficiently predict the large-scale clustering of matter and dark matter halos, given that we will have access to a wealth of information on scales beyond the linear regime. We inspect the extension of theoretical predictions for observable quantities in alternative cosmologies to CDM at fully nonlinear scales by means of -body simulations. We discuss the impact of relativistic corrections in extended cosmological models. Overall, this review highlights the significant potential of the Euclid mission to tightly constrain parameters of dark energy and modified gravity models, or perhaps to detect possible signatures of a CDM failure
Homogeneous spaces over an abelian variety
No full textIn this paper, we study a question of Colliot-Thélène and Iyer concerning the existence of rational sections in families of homogeneous spaces over an abelian variety, after base change by a suitable étale isogeny of the abelian variety. Assuming characteristic zero and that the homogeneous spaces arise from connected reductive groups, the problem is reformulated in terms of torsors under reductive groups over an abelian variety .Building on work of Moonen and Polishchuk, we construct a filtration on the motive of a Jacobian variety to analyze the action of isogenies on unramified cohomology and Witt groups. This approach allows for a positive response to the question for reductive groups whose root data do not contain a factor of type~ when \dim A > 2 and , and for all reductive groups when and is algebraically closed
Classical and relativistic balance of configurational forces
No full textThis article develops a unified variational framework for configurational (or material) forces in both Classical (3D, non-relativistic) and Relativistic (4D) Continuum Mechanics. Configurational forces describe the evolution of material defects-such as cracks, dislocations, and interfaces-which move relative to the material rather than through physical space. In the classical setting of hyperelasticity, the authors revisit the balance of configurational forces using an intrinsic Lagrangian formulation, where the material body is modeled as an abstract three-dimensional manifold. By treating the reference configuration as a variable and performing a Lagrangian variation with respect to it, they show that the configurational forces balance naturally emerges. Importantly, this balance equation is not independent: it is equivalent to the standard balance of linear momentum combined with constitutive relations, and it is expressed through the Eshelby stress tensor on the reference configuration. The framework is then extended to Relativistic Hyperelasticity within General Relativity. Matter is described by a matter field, a vector valued function, defined on the four-dimensional Universe, and the Lagrangian (i.e., Action) includes both matter and gravitational contributions. Two stress-energy tensors arise: the Noether stress-energy tensor (from variations with respect to the matter field) and the Hilbert stress-energy tensor (from variations with respect to the Universe metric). Assuming General Covariance, the authors prove that these tensors and their associated balance laws are equivalent. By introducing the notion of an observer and specializing to static spacetimes, the authors define a relativistic generalization of the deformation and derive a four-dimensional Eshelby tensor. They show that in Special Relativity, as in Classical Continuum Mechanics, the relativistic configurational forces balance is not a new equation but follows from the conservation laws of the Noether stress-energy tensor. Finally, they recover the classical configurational forces balance as the non-relativistic limit of the relativistic theory. Overall, the paper provides a rigorous geometric and variational interpretation of configurational forces, unifying classical and relativistic formulations and clarifying their deep connection with standard equilibrium equations.</div
Impact of physiological and biomechanical parameters on lung deformation and the accuracy of lung tumor motion estimation
No full textInternational audiencePatient-specific biomechanical models of the respiratory system can enhancethe prediction of lung tumor positions and deformations for radiation ther-apy. To achieve this, we have developed a patient-specific biomechanicalmodel of the entire respiratory system. However, the accuracy of the simula-tion is highly influenced by mechanical behavior as well as biomechanical andphysiological properties. In this study, we have investigated the impact ofsimplification and variability in mechanical and physiological property uncer-tainties on lung tumor motion prediction. Specifically, we have evaluated andcompared the most commonly used values of the lung tissue Young’s modulusand Poisson’s ratio found in the literature. Furthermore, we have examinedthe effect of a simple and fast linear compliance model versus a nonlinear,personalized physiological lung compliance model in computing lung and di-aphragm strain. We have also explored the impact of different nonlinearbehavior models to identify the most suitable mechanical model for respi-ratory simulation. To this end, we have conducted a study on four widelyreferenced hyperelastic models. Numerical simulations were performed onpublic datasets using the Neo-Hooke, Yeoh, Mooney-Rivlin, and St. Venant-Kirchhoff hyperelastic models. We have observed that nonlinear personalizedcompliance enhances accuracy and yields better results compared to linearcompliance. The simulations in this study showed minimal and negligiblevariations with different values of Young’s modulus. In contrast, variationsin Poisson’s ratio significantly impacted the simulation results. In our simula-tions, the Saint-Venant–Kirchhoff and Mooney–Rivlin models demonstratedthe highest accuracy for simulating lung tissue across all phases of respira-tion, with an average landmark error of 2.1 ± 1.3mm. This model has the potential to provide precise tumor motion predictions, helping physicians re-duce safety margins and minimize damage to healthy tissues during radiationtherapy
Modèles de fondation pour la segmentation d’images IRM cardiaque : une révolution en marche ?
No full textInternational audienceLa segmentation d'images médicales représente un défi clé dans le cadre d'applications cliniques comme l’aide au diagnostic. Le modèle nnUNet est devenu une référence grâce à ses performances de haute qualité et à sa capacité à s’adapter automatiquement aux bases de données médicales. Cependant, il nécessite un entraînement sur des centaines, voire des milliers de cas annotés, ce qui peut être fastidieux. Les modèles de fondation offrent une alternative prometteuse. Étant entraînés sur de vastes bases de données, ils semblent faire preuve d’une grande flexibilité, s’adaptant à de nouvelles données sans entraînement ou avec un nombre limité d’images annotées.Dans ce travail, nous comparons les performances de MedSAM, un modèle de fondation spécialisé dans la segmentation d’images médicales, à celles de nnUNet. Ces modèles sont évalués sur des bases de données IRM cardiaques en séquences ciné (ACDC) et rehaussement tardif (MYOSAIQ). Différentes stratégies d'entraînement de MedSAM et de SamMed2d sont testées afin de produire les meilleurs résultats possibles sur nos données. Des stratégies d’initialisation de boîtes englobantes (prompts) parfaites et avec 10 positions aléatoires autour du masque de référence sont investigués.Notre étude met en évidence les limites inhérentes aux modèles de fondation appliqués à la segmentation d’images médicales, notamment la dépendance des résultats à la qualité des prompts
Single-Asperity Friction and Wear in Seismic Faults: 2. DEM Simulations
No full textSeismic faults are rough, and their geometrical complexity is an important research topic. In this work, we present a numerical model dedicated to the simulation of friction and wear in an idealized fault asperity, taking inspiration from an experimental device used in a companion paper. The model can simulate the progressive damaging of the fault rock close to the contact, the release of fault gouge in the interface, and its circulation in the asperity and ejection from it. This allows to explore the complex interplay between a geometrical asperity and a gouge layer, in the presence of wear. Numerical results show that the asperity spontaneously evolves toward a tribological steady state in terms of friction, wear rate, roughness, and gouge thickness, in qualitative (and sometimes quantitative) agreement with experiments. We show that the existence of a geometrical asperity does not preclude the presence of a persistent gouge layer, which properties control the tribological response of the interface, and we emphasize the importance of understanding the mechanical, geometrical and rheological factors controlling its thickness
X-ray simulations with gVXR in education, digital twining, experiment planning, and data analysis
No full textInternational audiencegVirtualXray (gVXR) is an open-source framework that relies on the Beer-Lambert law to simulate X-ray images in real time on a graphics processor unit (GPU) using triangular meshes. A wide range of programming languages is supported (C/C++, Python, R, Ruby, Tcl, C#, Java, and GNU Octave). Simulations generated with gVXR have been benchmarked with clinically realistic phantoms (i.e. complex structures and materials) using Monte Carlo (MC) simulations, real radiographs and real digitally reconstructed radiographs (DRRs), and X-ray computed tomography (CT). It has been used in a wide range of applications, including real-time medical simulators, proposing a new densitometric radiographic modality in clinical imaging, studying noise removal techniques in fluoroscopy, teaching particle physics and X-ray imaging to undergraduate students in engineering, and XCT to masters students, predicting image quality and artifacts in material science, etc. gVXR has also been used to produce a high number of realistic simulated images in optimisation problems and to train machine learning algorithms. This paper presents a comprehensive review of such applications of gVXR
Minimax testing in a statistical inverse problem with unknown operator
No full textWe study minimax testing in a statistical inverse problem when the associated operator is unknown. In particular, we consider observations from an inverse Gaussian regression model where the associated operator is unknown but contained in a given dictionary B of finite cardinality. Using the non-asymptotic framework for minimax testing (that is, for any fixed value of the noise level), we provide optimal separation conditions for the goodness-of-fit testing problem. We restrict our attention to the specific case where the dictionary contains only two members. As we will demonstrate, even this simple case is quite intrigued and reveals an interesting phase transition phenomenon. The general case is even more involved, requires different strategies, and it is only briefly discussed