The Gaia Galactic survey mission is designed and optimized to obtain astrometry, photometry, and spectroscopy of nearly two billion stars in our Galaxy. Yet as an all-sky multi-epoch survey, Gaia also observes several million extragalactic objects down to a magnitude of G~21 mag. Due to the nature of the Gaia onboard selection algorithms, these are mostly point-source-like objects. Using data provided by the satellite, we have identified quasar and galaxy candidates via supervised machine learning methods, and estimate their redshifts using the low resolution BP/RP spectra. We further characterise the surface brightness profiles of host galaxies of quasars and of galaxies from pre-defined input lists. Here we give an overview of the processing of extragalactic objects, describe the data products in Gaia DR3, and analyse their properties. Two integrated tables contain the main results for a high completeness, but low purity (50-70%), set of 6.6 million candidate quasars and 4.8 million candidate galaxies. We provide queries that select purer sub-samples of these containing 1.9 million probable quasars and 2.9 million probable galaxies (both 95% purity). We also use high quality BP/RP spectra of 43 thousand high probability quasars over the redshift range 0.05-4.36 to construct a composite quasar spectrum spanning restframe wavelengths from 72-100 nm.

We investigate the existence of densities for finite-dimensional distributions of Hermite processes of order $q \ge 1$ and self-similarity parameter $H\in(\frac12,1)$. Whereas the Gaussian case $q=1$ (fractional Brownian motion) is well understood, the non-Gaussian situation has not yet been settled. In this work, we extend the classical three-step approach used in the Gaussian case: factorization of the determinant into conditional terms, strong local nondeterminism, and non-degeneracy. We transport this strategy to the Hermite setting using Malliavin calculus. Specifically, we establish a determinant identity for the Malliavin matrix, prove strong local nondeterminism at the level of Malliavin derivatives, and apply the Bouleau-Hirsch criterion. Consequently, for any distinct times $t_1,\dots,t_n$, the vector $(Z^{H,q}_{t_1},\dots,Z^{H,q}_{t_n})$ of a Hermite process admits a density with respect to the Lebesgue measure. Beyond the result itself, the main contribution is the methodology, which could extend to other non-Gaussian models.

A scalar ultralight dark matter (ULDM) candidate would induce oscillatory motion of freely falling test masses via its coupling to Standard Model fields. Such oscillations would create an observable Doppler shift of light exchanged between the test masses, and in particular would be visible in space-based gravitational waves (GW) detectors, such as LISA. While this kind of detection has been proposed multiple times in the recent years, we numerically investigate if it is possible to extract a scalar ULDM signal in a space-based GW detector, and in particular how to differentiate such a signal from a GW signal. Using one year of realistic orbits for the LISA spacecrafts and Bayesian methods, we find that LISA will indeed be able to discriminate between the two signals.

Aerosol forecasting is essential for air quality warnings, health risk assessment, and climate change mitigation. However, it is more complex than weather forecasting due to the intricate interactions between aerosol physicochemical processes and atmospheric dynamics, resulting in significant uncertainty and high computational costs. Here, we develop an artificial intelligence-driven global aerosol-meteorology forecasting system (AI-GAMFS), which provides reliable 5-day, 3-hourly forecasts of aerosol optical components and surface concentrations at a 0.5° x 0.625° resolution. AI-GAMFS combines Vision Transformer and U-Net in a backbone network, robustly capturing the complex aerosol-meteorology interactions via global attention and spatiotemporal encoding. Trained on 42 years of advanced aerosol reanalysis data and initialized with GEOS Forward Processing (GEOS-FP) analyses, AI-GAMFS delivers operational 5-day forecasts in one minute. It outperforms the Copernicus Atmosphere Monitoring Service (CAMS) global forecasting system, GEOS-FP forecasts, and several regional dust forecasting systems in forecasting most aerosol variables including aerosol optical depth and dust components. Our results mark a significant step forward in leveraging AI to refine physics-based aerosol forecasting, facilitating more accurate global warnings for aerosol pollution events, such as dust storms and wildfires.

We investigate diffusion models to solve the Traveling Salesman Problem. Building on the recent DIFUSCO and T2TCO approaches, we propose IDEQ. IDEQ improves the quality of the solutions by leveraging the constrained structure of the state space of the TSP. Another key component of IDEQ consists in replacing the last stages of DIFUSCO curriculum learning by considering a uniform distribution over the Hamiltonian tours whose orbits by the 2-opt operator converge to the optimal solution as the training objective. Our experiments show that IDEQ improves the state of the art for such neural network based techniques on synthetic instances. More importantly, our experiments show that IDEQ performs very well on the instances of the TSPlib, a reference benchmark in the TSP community: it closely matches the performance of the best heuristics, LKH3, being even able to obtain better solutions than LKH3 on 2 instances of the TSPlib defined on 1577 and 3795 cities. IDEQ obtains 0.3% optimality gap on TSP instances made of 500 cities, and 0.5% on TSP instances with 1000 cities. This sets a new SOTA for neural based methods solving the TSP. Moreover, IDEQ exhibits a lower variance and better scales-up with the number of cities with regards to DIFUSCO and T2TCO.

Analog in-memory computing is an emerging paradigm designed to efficiently accelerate deep neural network workloads. Recent advancements have focused on either inference or training acceleration. However, a unified analog in-memory technology platform-capable of on-chip training, weight retention, and long-term inference acceleration-has yet to be reported. This work presents an all-in-one analog AI accelerator, combining these capabilities to enable energy-efficient, continuously adaptable AI systems. The platform leverages an array of analog filamentary conductive-metal-oxide (CMO)/HfOx resistive switching memory cells (ReRAM) integrated into the back-end-of-line (BEOL). The array demonstrates reliable resistive switching with voltage amplitudes below 1.5V, compatible with advanced technology nodes. The array multi-bit capability (over 32 stable states) and low programming noise (down to 10nS) enable a nearly ideal weight transfer process, more than an order of magnitude better than other memristive technologies. Inference performance is validated through matrix-vector multiplication simulations on a 64x64 array, achieving a root-mean-square error improvement by a factor of 20 at 1 second and 3 at 10 years after programming, compared to state-of-the-art. Training accuracy closely matching the software equivalent is achieved across different datasets. The CMO/HfOx ReRAM technology lays the foundation for efficient analog systems accelerating both inference and training in deep neural networks.

Robust distributed learning algorithms aim to maintain reliable performance despite the presence of misbehaving workers. Such misbehaviors are commonly modeled as Byzantine failures, allowing arbitrarily corrupted communication, or as data poisoning, a weaker form of corruption restricted to local training data. While prior work shows similar optimization guarantees for both models, an important question remains: How do these threat models impact generalization? Empirical evidence suggests a gap, yet it remains unclear whether it is unavoidable or merely an artifact of suboptimal attacks. We show, for the first time, a fundamental gap in generalization guarantees between the two threat models: Byzantine failures yield strictly worse rates than those achievable under data poisoning. Our findings leverage a tight algorithmic stability analysis of robust distributed learning. Specifically, we prove that: (i) under data poisoning, the uniform algorithmic stability of an algorithm with optimal optimization guarantees degrades by an additive factor of $\varTheta ( \frac{f}{n-f} )$, with $f$ out of $n$ workers misbehaving; whereas $\textit{(ii)}$ under Byzantine failures, the degradation is in $\Omega \big( \sqrt{ \frac{f}{n-2f}} \big)$.

Three ring systems have been discovered to date around small irregular objects of the solar system (Chariklo, Haumea and Quaoar). For the three bodies, material is observed near the second-order 1/3 Spin-Orbit Resonance (SOR) with the central object, and in the case of Quaoar, a ring is also observed near the second-order resonance 5/7 SOR. This suggests that second-order SORs may play a central role in ring confinement. This paper aims at better understanding this role from a theoretical point of view. It also provides a basis to better interpret the results obtained from N-body simulations and presented in a companion paper. A Hamiltonian approach yields the topological structure of phase portraits for SORs of orders from one to five. Two cases of non-axisymmetric potentials are examined: a triaxial ellipsoid characterized by an elongation parameter C22 and a body with mass anomaly mu, a dimensionless parameter that measures the dipole component of the body's gravitational field. The estimated triaxial shape of Chariklo shows that its corotation points are marginally unstable, those of Haumea are largely unstable, while those of Quaoar are safely stable. The topologies of the phase portraits show that only first- (aka Lindblad) and second-order SORs can significantly perturb a dissipative collisional ring. We calculate the widths, the maximum eccentricities and excitation time scales associated with first- and second-order SORs, as a function of C22 and mu. Applications to Chariklo, Haumea and Quaoar using mu ~ 0.001 show that the first- and second-order SORs caused by their triaxial shapes excite large (>~ 0.1) orbital eccentricities on the particles, making the regions inside the 1/2 SOR inhospitable for rings. Conversely, the 1/3 and 5/7 SORs caused by mass anomalies excite moderate eccentricities (<~ 0.01), and are thus a more favorable place for the presence of a ring.

This paper introduces a general multi-agent bandit model in which each agent is facing a finite set of arms and may communicate with other agents through a central controller in order to identify, in pure exploration, or play, in regret minimization, its optimal arm. The twist is that the optimal arm for each agent is the arm with largest expected mixed reward, where the mixed reward of an arm is a weighted sum of the rewards of this arm for all agents. This makes communication between agents often necessary. This general setting allows to recover and extend several recent models for collaborative bandit learning, including the recently proposed federated learning with personalization (Shi et al., 2021). In this paper, we provide new lower bounds on the sample complexity of pure exploration and on the regret. We then propose a near-optimal algorithm for pure exploration. This algorithm is based on phased elimination with two novel ingredients: a data-dependent sampling scheme within each phase, aimed at matching a relaxation of the lower bound.

Over the past two decades, machine analysis of medical imaging has advanced rapidly, opening up significant potential for several important medical applications. As complicated diseases increase and the number of cases rises, the role of machine-based imaging analysis has become indispensable. It serves as both a tool and an assistant to medical experts, providing valuable insights and guidance. A particularly challenging task in this area is lesion segmentation, a task that is challenging even for experienced radiologists. The complexity of this task highlights the urgent need for robust machine learning approaches to support medical staff. In response, we present our novel solution: the D-TrAttUnet architecture. This framework is based on the observation that different diseases often target specific organs. Our architecture includes an encoder-decoder structure with a composite Transformer-CNN encoder and dual decoders. The encoder includes two paths: the Transformer path and the Encoders Fusion Module path. The Dual-Decoder configuration uses two identical decoders, each with attention gates. This allows the model to simultaneously segment lesions and organs and integrate their segmentation losses. To validate our approach, we performed evaluations on the Covid-19 and Bone Metastasis segmentation tasks. We also investigated the adaptability of the model by testing it without the second decoder in the segmentation of glands and nuclei. The results confirmed the superiority of our approach, especially in Covid-19 infections and the segmentation of bone metastases. In addition, the hybrid encoder showed exceptional performance in the segmentation of glands and nuclei, solidifying its role in modern medical image analysis.

Multi-objective parametric optimization problem is presented for overwrapped composite pressure vessels under internal pressure for storage and heating water. It is solved using the developed iterative optimization algorithm. Optimal values of design parameters for the vessel are obtained by varying the set of parameters for composite layers, such as the thickness of layers and radii of polar openings, which influence the distribution of fiber angles along the vessel. The suggested optimization methodology is based on the mechanical solution for composite vessels and the satisfaction of the main failure criteria. An innovative approach lies in the possibility of using the developed optimization methodology for designing vessels with non-symmetrical filament winding, which have unequal polar openings on the domes. This became possible due to the development of a special numerical mechanical finite element model of a composite vessel. A specific Python program provides the creation of a model and controls the exchange of data between the modules of the iterative optimization process. The numerical model includes the determination of the distribution of fiber angles on the domes and cylindrical part of the vessel as well as changes in layer thicknesses. The optimization problem solution is provided using a Multi-Island Genetic Algorithm, this type of method showed its efficiency for such applications, by allowing to avoid local solutions. Thus, optimal parameters of a composite vessel were found by minimizing composite mass and thickness and maximizing the strain energy. Test solutions using the developed methodology are presented for three types of composite materials to evaluate their possibility for integration into the vessel design model.

We investigate rigidity phenomena in one-dimensional point processes. We show that the existence of an $L^1$ transport map from a stationary lattice or the Lebesgue measure to a point process is sufficient to guarantee the properties of Number-Rigidity and Cyclic-Factor. We then apply this result to non-singular Riesz gases with parameter $s\in(-2,-1]$, defined in infinite volume as accumulation points of stationarized finite-volume Riesz gases. This includes, for $s=-1$, the well-known one-dimensional Coulomb gas (also called Jellium plasma, or the one-component 1D plasma).

This user's guide (updated version) consists of two parts. The first part is an extensive survey contributed to the Encyclopedia of Mathematical Physics, 2nd edition. It covers many of the main constructions, definitions, and applications of the classical configuration spaces of points. The second part delves into the geometry of chromatic configuration spaces, giving a detailed proof of the remarkable result that the Poincar\'e polynomial of the chromatic configuration spaces of $\mathbb R^N$, associated to a finite simple graph $\Gamma$, corresponds to the reciprocal of the chromatic polynomial of the graph (with signs). Further applications and a stable splitting are given.

Emergency departments struggle with persistent triage errors, especially undertriage and overtriage, which are aggravated by growing patient volumes and staff shortages. This study evaluated three AI models [TRIAGEMASTER (NLP), URGENTIAPARSE (LLM), and EMERGINET (JEPA)] against the FRENCH triage scale and nurse practice, using seven months of adult triage data from Roger Salengro Hospital in Lille, France. Among the models, the LLM-based URGENTIAPARSE consistently outperformed both AI alternatives and nurse triage, achieving the highest accuracy (F1-score 0.900, AUC-ROC 0.879) and superior performance in predicting hospitalization needs (GEMSA). Its robustness across structured data and raw transcripts highlighted the advantage of LLM architectures in abstracting patient information. Overall, the findings suggest that integrating LLM-based AI into emergency department workflows could significantly enhance patient safety and operational efficiency, though successful adoption will depend on addressing limitations and ensuring ethical transparency.

Aircraft performance models play a key role in airline operations, especially in planning a fuel-efficient flight. In practice, manufacturers provide guidelines which are slightly modified throughout the aircraft life cycle via the tuning of a single factor, enabling better fuel predictions. However this has limitations, in particular they do not reflect the evolution of each feature impacting the aircraft performance. Our goal here is to overcome this limitation. The key contribution of the present article is to foster the use of machine learning to leverage the massive amounts of data continuously recorded during flights performed by an aircraft and provide models reflecting its actual and individual performance. We illustrate our approach by focusing on the estimation of the drag and lift coefficients from recorded flight data. As these coefficients are not directly recorded, we resort to aerodynamics approximations. As a safety check, we provide bounds to assess the accuracy of both the aerodynamics approximation and the statistical performance of our approach. We provide numerical results on a collection of machine learning algorithms. We report excellent accuracy on real-life data and exhibit empirical evidence to support our modelling, in coherence with aerodynamics principles.

In supervised learning, decision trees are valued for their interpretability and performance. While greedy decision tree algorithms like CART remain widely used due to their computational efficiency, they often produce sub-optimal solutions with respect to a regularized training loss. Conversely, optimal decision tree methods can find better solutions but are computationally intensive and typically limited to shallow trees or binary features. We present Dynamic Programming Decision Trees (DPDT), a framework that bridges the gap between greedy and optimal approaches. DPDT relies on a Markov Decision Process formulation combined with heuristic split generation to construct near-optimal decision trees with significantly reduced computational complexity. Our approach dynamically limits the set of admissible splits at each node while directly optimizing the tree regularized training loss. Theoretical analysis demonstrates that DPDT can minimize regularized training losses at least as well as CART. Our empirical study shows on multiple datasets that DPDT achieves near-optimal loss with orders of magnitude fewer operations than existing optimal solvers. More importantly, extensive benchmarking suggests statistically significant improvements of DPDT over both CART and optimal decision trees in terms of generalization to unseen data. We demonstrate DPDT practicality through applications to boosting, where it consistently outperforms baselines. Our framework provides a promising direction for developing efficient, near-optimal decision tree algorithms that scale to practical applications.