US assembles the most aerial firepower since Iraq War as Trump prepares to strike Iran'in just DAYS'... and president is'choosing between two devastating options of attack' Model agency boss who'scouted' victims for Epstein was secretly planning to testify against him... only to suddenly change his mind before meeting chillingly similar fate to notorious pedophile The monarchy has survived wars and countless crises... but this is why it may not survive Andrew's arrest - and why the rift at the heart of the family is about to get so much worse: ROBERT JOBSON But countless women (and some husbands) are secretly getting it for thrilling sex side effects... risking a truly putrid complication FBI'has names and photos of people who may be masked suspect caught on surveillance video outside Nancy Guthrie's home' Widower whose wife set herself on fire after alleged affair with married congressman finally breaks silence to reveal their texts... and heartbreaking video of her death The side-effects were unbearable and I swore off the drug forever. This is the simple diet that helped me shed the pounds... and I'm not alone. Lindsey Vonn shares nervous post as she awaits fifth surgery on broken leg after Olympic fall and dog's death Jason Bateman says he quit cocaine and alcohol to ease'tension' in his marriage Humiliating real reason Mia Goth left Shia LaBeouf: What'friends and lovers' are all saying behind his back... after Mardi Gras brawl Turmoil ramps up at Today Show as Hoda ditches her'family first' exit to reclaim her coveted anchor seat.... whether Savannah returns or not Whereabouts of Andrew's ex-wife and daughters remain unknown as former prince is arrested over public misconduct claims Peter Greene's cause of death revealed two months after Pulp Fiction star was found dead at 60 in NYC apartment Tucker Carlson'DETAINED' in Israel: Journalist'dragged into interrogation room' as explosive interview sparks diplomatic firestorm My teenage son picked up a dirty habit to'look cool' in front of his friends. He was rushed to hospital with deadly lung condition now I'm issuing an urgent plea What happens now Andrew Mountbatten-Windsor has been arrested? Germany's army chief warns Europe will suffer'things we cannot even imagine right now' as Putin looks to go to war with Europe - and slams'egomaniac' Trump Scientists confirm wet weather slashes life satisfaction by 6% - as soggy Brits vent they're'flipping sick of it' READ MORE: You think this is bad?

A.I. re-creations of the "Magnificent Ambersons" stars Joseph Cotten, Agnes Moorehead, Dolores Costello, and Tim Holt. Edward Saatchi first saw "The Magnificent Ambersons," Orson Welles's mangled masterpiece from 1942, when he was twelve years old, in the private screening room of his family's crenellated mansion, in West Sussex. Saatchi's parents had already shown him and his brother "Citizen Kane." But "Ambersons," Welles's follow-up film, about a wealthy Midwestern clan brought low, came with a bewitching backstory: R.K.O. had ripped the movie from the director's hands, slashed forty-three minutes, tacked on a happy ending, and destroyed the excised footage in order to free up vault space, leaving decades' worth of cinephiles to obsess over what might have been. Part of this outcome was the result of studio treachery, but Welles, owing to some combination of hubris and distraction, had let his film slip from his grasp. Saatchi recalled, "Around the family dinner table, that was always such a big topic: How much was Welles responsible for this? Mum was always quite tough on him." Saatchi's father, Maurice, a baron also known as Lord Saatchi, is one of two Iraqi British brothers who founded the advertising firm Saatchi & Saatchi, in 1970, which led their family to become one of the richest in the U.K. Edward's mother, Josephine Hart, who died in 2011, was an Irish writer best known for her erotic thriller "Damage," which was adapted into a film by Louis Malle. Edward, born in 1985, grew up in London and at the sprawling country estate, surrounded by palatial gardens and classical statuary. He described his parents as "movie mad." The actor and Welles biographer Simon Callow, a Saatchi family friend, recalled, "They had a cinema of their own inside the house, and it was a ritual of theirs every week to watch a film together." Aside from old movies, Edward was obsessed with "Star Trek"--especially the Holodeck, a device that conjured simulated 3-D worlds populated by characters who could interact with the members of the Starship Enterprise. That kind of wizardry didn't exist in the real world, at least not yet. But the young prince of the Saatchi castle had faith that someday it would, and that it could bring the original "Ambersons" back from oblivion. "To me, this is the lost holy grail of cinema," Saatchi told me recently, like Charles Foster Kane murmuring about Rosebud. "It just seemed intuitively that there would be some way to undo what had happened."

Distributionally robust optimisation (DRO) minimises the worst-case expected loss over an ambiguity set that can capture distributional shifts in out-of-sample environments. While Huber (linear-vacuous) contamination is a classical minimal-assumption model for an $\varepsilon$-fraction of arbitrary perturbations, including it in an ambiguity set can make the worst-case risk infinite and the DRO objective vacuous unless one imposes strong boundedness or support assumptions. We address these challenges by introducing bulk-calibrated credal ambiguity sets: we learn a high-mass bulk set from data while considering contamination inside the bulk and bounding the remaining tail contribution separately. This leads to a closed-form, finite $\mathrm{mean}+\sup$ robust objective and tractable linear or second-order cone programs for common losses and bulk geometries. Through this framework, we highlight and exploit the equivalence between the imprecise probability (IP) notion of upper expectation and the worst-case risk, demonstrating how IP credal sets translate into DRO objectives with interpretable tolerance levels. Experiments on heavy-tailed inventory control, geographically shifted house-price regression, and demographically shifted text classification show competitive robustness-accuracy trade-offs and efficient optimisation times, using Bayesian, frequentist, or empirical reference distributions.

We introduce Neural Optimal Design of Experiments, a learning-based framework for optimal experimental design in inverse problems that avoids classical bilevel optimization and indirect sparsity regularization. NODE jointly trains a neural reconstruction model and a fixed-budget set of continuous design variables representing sensor locations, sampling times, or measurement angles, within a single optimization loop. By optimizing measurement locations directly rather than weighting a dense grid of candidates, the proposed approach enforces sparsity by design, eliminates the need for l1 tuning, and substantially reduces computational complexity. We validate NODE on an analytically tractable exponential growth benchmark, on MNIST image sampling, and illustrate its effectiveness on a real world sparse view X ray CT example. In all cases, NODE outperforms baseline approaches, demonstrating improved reconstruction accuracy and task-specific performance.

We show that quantum oracles provide an advantage over classical oracles for answering classical counterfactual questions in causal models, or equivalently, for identifying unknown causal parameters such as distributions over functional dependences. In structural causal models with discrete classical variables, observational data and even ideal interventions generally fail to answer all counterfactual questions, since different causal parameters can reproduce the same observational and interventional data while disagreeing on counterfactuals. Using a simple binary example, we demonstrate that if the classical variables of interest are encoded in quantum systems and the causal dependence among them is encoded in a quantum oracle, coherently querying the oracle enables the identification of all causal parameters -- hence all classical counterfactuals. We generalize this to arbitrary finite cardinalities and prove that coherent probing 1) allows the identification of all two-way joint counterfactuals p(Y_x=y, Y_{x'}=y'), which is not possible with any number of queries to a classical oracle, and 2) provides tighter bounds on higher-order multi-way counterfactuals than with a classical oracle. This work can also be viewed as an extension to traditional quantum oracle problems such as Deutsch--Jozsa to identifying more causal parameters beyond just, e.g., whether a function is constant or balanced. Finally, we raise the question of whether this quantum advantage relies on uniquely non-classical features like contextuality. We provide some evidence against this by showing that in the binary case, oracles in some classically-explainable theories like Spekkens' toy theory also give rise to a counterfactual identifiability advantage over strictly classical oracles.

Random Forests and Gradient Boosting are among the most effective algorithms for supervised learning on tabular data. Both belong to the class of tree-based ensemble methods, where predictions are obtained by aggregating many randomized regression trees. In this paper, we develop a theoretical framework for analyzing such methods through Reproducing Kernel Hilbert Spaces (RKHSs) constructed on tree ensembles--more precisely, on the random partitions generated by randomized regression trees. We establish fundamental analytical properties of the resulting Random Forest kernel, including boundedness, continuity, and universality, and show that a Random Forest predictor can be characterized as the unique minimizer of a penalized empirical risk functional in this RKHS, providing a variational interpretation of ensemble learning. We further extend this perspective to the continuous-time formulation of Gradient Boosting introduced by Dombry and Duchamps (2024a,b), and demonstrate that it corresponds to a gradient flow on a Hilbert manifold induced by the Random Forest RKHS. A key feature of this framework is that both the kernel and the RKHS geometry are data-dependent, offering a theoretical explanation for the strong empirical performance of tree-based ensembles. Finally, we illustrate the practical potential of this approach by introducing a kernel principal component analysis built on the Random Forest kernel, which enhances the interpretability of ensemble models, as well as GVI, a new geometric variable importance criterion.

Thousands of Airbus planes are being returned to normal service after being grounded for hours due to a warning that solar radiation could interfere with onboard flight control computers. The aerospace giant - based in France - said around 6,000 of its A320 planes had been affected with most requiring a quick software update. Some 900 older planes need a replacement computer. French Transport Minister Philippe Tabarot said the updates went very smoothly for more than 5,000 planes. Fewer than 100 aircraft still needed the update, Airbus had told him, according to local media.

No, your favourite influencer hasn't got a dozen dachshund dogs. When scrolling through social media recently, you might have noticed posts which seem a bit off. It's all AI generated and due to its low quality and its inauthenticity, it's being branded AI slop. Both social media users and content creators say they're worried that AI slop flooding feeds is leading to a less authentic online experience - and is drowning out real posts. But a new trend, which sees people adding AI-generated animals to original photographs, has encouraged some content creators to embrace AI.

ABSTRACT Scientific datasets often arise from multiple independent mechanisms such as spati al, categorical or structural effects, whose combined influence obscures their individual contributions. We introduce DIVIDE, a framework that disentangles these influences by integrating mechanism - specific deep encoders with a structured Gaussian Process in a joint latent space. Disentanglement here refers to separating independently acting generative factors . The encoders isolate distinct mechanisms while the Gaussian Process captures their combined effect with calibrated uncertainty. The architecture supports structured priors, enabling interpretable and mechanism - aware prediction as well as efficient active l earning. Across benc hmarks, DIVIDE separates mechanisms, reproduces additive and scaled interactions, and remains robust under noise. The framework extends naturally to multifunctional datasets where mechanical, electromagnetic or optical responses coexist. INTRODUCTION Many real - world systems exhibit behavior driven by the combined influence of multiple independent mechanisms. These mechanisms may represent categorical factors, spatial dependencies, or nonlinear physical responses. While the scalar output of such systems is observable, the individual contributions of these mechanisms are often unknown and unmeasured. Modeling this type of data requires not only accurate predictions but also the ability to attribute variation in the output to specific, distinct sources. In thi s context, we use disentanglement to mean recovering those independently acting generative factors from observational data. Disentangling these contributions is particularly important in scientific and engineering domains where interpretability, causality, and mechanism - aware reasoning are essential. Partial solutions to this challenge have emerged from the field of disentangled representation learning, which seeks to identify independent factors of variation from high - dimensional data.

Many manifold embedding algorithms fail apparently when the data manifold has a large aspect ratio (such as a long, thin strip). Here, we formulate success and failure in terms of finding a smooth embedding, showing also that the problem is pervasive and more complex than previously recognized.