Université Côte d'Azur

We prove oracle inequalities for a penalized log-likelihood criterion that hold even if the data are not independent and not stationary, based on a martingale approach. The assumptions are checked for various contexts: density estimation with independent and identically distributed (i.i.d) data, hidden Markov models, spiking neural networks, adversarial bandits. In each case, we compare our results to the literature, showing that, although we lose some logarithmic factors in the most classical case (i.i.d.), these results are comparable or more general than the existing results in the more dependent cases.

Water and land surfaces on a planet interact in particular ways with gases in the atmosphere and with radiation from the star. These interactions define the environments that prevail on the planet, some of which may be more amenable to prebiotic chemistry, some to the evolution of more complex life. This review article covers (i) the physical conditions that determine the ratio of land to sea on a rocky planet, (ii) how this ratio would affect climatic and biologic processes, and (iii) whether future astronomical observations might constrain this ratio on exoplanets. Water can be delivered in multiple ways to a growing rocky planet — and although we may not agree on the contribution of different mechanism(s) to Earth’s bulk water, hydrated building blocks and nebular ingassing could at least in principle supply several oceans’ worth. The water that planets can sequester over eons in their solid deep mantles is limited by the water concentration at water saturation of nominally anhydrous mantle minerals, being in sum likely less than 2000 ppm of the planet mass. Water is cycled between mantle and surface through outgassing and ingassing mechanisms that, while tightly linked to tectonics, do not necessarily require plate tectonics in every case. The actual water/land ratio at a given time then emerges from the balance between the volume of surface water on the one hand, and on the other hand, the shape of the planet (its ocean basin volume) that is carved out by dynamic topography, the petrologic evolution of continents, impact cratering, and other surface-sculpting processes. By leveraging the contrast in reflectance properties of water and land surfaces, spatially resolved 2D maps of Earth-as-an-exoplanet have been retrieved from models using real Earth observations, demonstrating that water/land ratios of rocky exoplanets may be determined from data delivered by large-aperture, high-contrast imaging telescopes in the future.

Data management in healthcare faces significant challenges in balancing security and anonymity during information exchange. Recent advancements in decentralized distributed ledgers and digital twins offer promising solutions to enhance knowledge sharing. A predictive digital twin creates a virtual model using data from various stakeholders to forecast outcomes, support decision-making for efficient resource allocation, and benchmark operational effectiveness. Digital twins can leverage blockchain technology to enable secure and decentralized data exchange while ensuring privacy and regulatory compliance. This paper introduces a novel dynamic blockchain-integrated predictive digital twin model aimed at improving information sharing and fostering collaboration among healthcare providers and stakeholders. Using federated learning, each provider site independently trains its model and shares aggregated insights to benchmark performance against peers. This collaborative approach encourages knowledge sharing and helps identify areas for operational improvement. Our dynamic and iterative approach is validated through three distinct applications: digitized cancer images, voice recordings from Parkinson’s disease patients, and a more generalized application for collaborative supplier selection, evaluating factors such as price, quality, and customer feedback. We find that federated learning can offer a robust and stable level of performance, as a valuable compromise between fully local and centralized learning approaches. By allowing healthcare institutions to collaborate without compromising patient confidentiality, federated learning improves prediction accuracy and overall outcomes. Our solution enables secure, privacy-preserving collaboration among healthcare institutions, allowing them to compare models, identify best practices, and improve operational effectiveness. Thus, our study makes an original contribution to improving healthcare cost-effectiveness through digital twins, with implications for personalized medicine and promoting interoperability.

The purpose of this article is to show that an intrinsic noise with values in the space 𝒫(ℝ) of 1d probability measures may force uniqueness to first order mean field games. The structure of the noise is inspired from the earlier work (Delarue and Hammersley in Probab Theory Relat Fields 191(1–2):41–102, 2025) . It reads as a coloured Ornstein-Uhlenbeck process with reflection on the boundary of quantile functions on the 1d torus, with the elements of the latter playing the role of indices for the continuum of players underpinning the game. In Delarue and Hammersley (Probab Theory Relat Fields 191(1–2):41–102, 2025), the semi-group generated by the noise is shown to enjoy smoothing properties that become key in the study carried out here. Although the analysis is limited to the 1d setting, this is the first example of uniqueness forcing for generic mean field games set over an infinite dimensional set of probability measures and this may be one step forward towards a more systematic regularization by noise theory for mean field games.

Operationalizing social justice is challenged by the absence of a universal equity definition and inherent policy trade-offs. This study bridges theoretical social justice principles with operational decision-making by integrating four commonly discussed distributive justice theories—Utilitarianism, Rawls’ Egalitarianism, Prioritarianism, and Capabilitarian Sufficiency—into a bilevel bus frequency optimization model. It introduces linearized equity-oriented formulations to reflect the distinct distributive principles of these theories and proposes justice theory-driven equity metrics to evaluate distributive impacts using different ethical criteria. Using cumulative opportunity as a unit of distribution, the proposed frameworks and metrics are applied to Canberra’s southern suburbs. The results demonstrate that the choice of justice framework is not a neutral modelling decision but a normative one, with each framework producing distinct redistributive patterns and community-level trade-offs. This highlights the importance of aligning equity frameworks with policy objectives and governance contexts, as these choices ultimately shape public perception, political feasibility, and the long-term societal goals of transport investment.