巴黎萨克雷大学

Lp spaces of mappings taking values in arbitrary metric spaces, which we call nonlinear Lebesgue spaces, play an important role in several fields of mathematics. For instance, membership in these spaces is typically required for transport maps in optimal transport theory and for stochastic processes in probability theory. Nonlinear Lebesgue spaces also arise naturally in applications such as medical imaging, where the physical signals at play often exhibit little regularity and take their values in nonlinear spaces. Yet, these spaces remain little studied in the literature, likely due to their lack of differential structure outside the case where mappings are valued in a linear space. This paper is the first in a series devoted to the study of geometric and analytic properties of nonlinear Lebesgue spaces. The present article exposes a systematic treatment of their measure-theoretic properties, unifying and refining scattered results from the literature while also extending classical results from the linear setting to this broader nonlinear framework—including the characterizations of their completeness and their separability as well as the density of some of their subspaces: the spaces of simple, continuous and smooth mappings.

Estimating excursion set confidence regions seeks to identify regions where a function may exceed some threshold with a given confidence level. This paper focuses on estimating such confidence regions in cases where the function has random inputs and a functional output that is returned all at once. We develop a surrogate-based approach for estimating the confidence region, combining principal component analysis and Gaussian process regression. An active learning strategy is also introduced, based on a max–min criterion that selects new samples which are likely to reduce the uncertainty in the confidence region. This strategy leverages efficient sampling of the Gaussian process through a Karhunen-Loève expansion.The proposed approach is applied to estimate the confidence regions of three case studies: a synthetic function, the surface pressure coefficient distribution of a hypersonic vehicle, and the glide-back trajectory of a reusable launcher first stage. The method demonstrates efficiency in accurately estimating the confidence region while reducing sources of modeling uncertainties. It is benchmarked against reference methods from the literature. Relevant metrics for assessing the confidence region estimation performance are discussed.

Physics-Based Loss Scaling (PBLS) is introduced for Mixed-Formulation PINNs (MF-PINNs) applied to the neutron diffusion equation. In particular, we propose a new scaled loss function based on the material cross sections, which is equivalent to the classical MF-PINN loss, but accelerates the convergence and improves accuracy of MF-PINNs. Several numerical experiments on both the fixed source and the k-eigenvalue problem, from one-group to multigroup cases and from two-dimensional (2D) to three-dimensional (3D) configurations, illustrate the efficiency of the proposed scaling method.

The rapid growth of satellite constellations has intensified the production pace in civil satellite battery manufacturing under stringent reliability requirements. To enhance responsiveness, manufacturers are shifting from single-factory to distributed architectures that parallelize assembly among sub-factories. This study investigates a distributed flowshop scheduling problem (DFSP) with learning effects, in which the release date of each assembly task is determined by material procurement. The objectives are to minimize maximum lateness and makespan, striking a balance between customer satisfaction and production efficiency. Since the joint impact of learning effects, release-date constraints, and the maximum lateness criterion has not been systematically investigated in the DFSP, this study first examines a single-objective DFSP to identify structural properties of the problem. A Branch-and-Price algorithm is proposed to optimally solve the DFSP with learning effects and release dates for minimizing maximum lateness, incorporating an upper-bound-based variable elimination and a Branch-and-Bound sub-solver to enhance computational efficiency. For the multi-objective DFSP, an iterative greedy algorithm is designed to attain high-quality solutions within limited computational time. Guided by insights from the single-objective analysis, resource-availability-driven initialization and critical-task-based search operators are introduced to exploit release-date and lateness characteristics, thereby improving search efficiency. Extensive experiments validate the effectiveness of the proposed algorithms. Although high-quality solutions have been reported, optimality remains unverified for many DFSP benchmark instances. By adapting the proposed Branch-and-Price to the benchmark setting, optimality is established for 129 out of 180 instances within a time limit of 1 hour per instance, none of which had previously been solved to optimality.

Antibody–drug conjugates (ADCs) are complex molecules composed of a monoclonal antibody, a linker and a cytotoxic payload. Their design enables the selective delivery of cytotoxic agents to tumoral cells through antibody binding to a tumor-expressed antigen, followed by internalization, intracellular degradation and payload release, ultimately enabling the cytotoxic drug to exert its antitumor activity. ADCs have been evaluated in phase II and III trials in previously treated advanced non-small cell lung cancer (NSCLC), both in oncogene-addicted and in non-oncogene-addicted tumors, addressing resistance to standard therapies. Ongoing clinical trials are now expanding their use both in the first-line setting for advanced disease and in earlier disease stages. This narrative review summarizes the currently available data for ADC treatment in NSCLC, highlighting the need for improved patient selection to maximize benefit while limiting toxicity, incorporating clinical characteristics, pharmacogenomics and optimal treatment sequencing in the equation. Moreover, the understanding of resistance mechanisms and the development and validation of predictive biomarkers will be of utmost relevance to inform clinical practice.