Recent weeks have seen a significant escalation of military tensions in and around the Baltics. Lithuania, Latvia and Estonia, which are all NATO members, now experience regular incursions into their airspace by Ukrainian drones. According to both Kyiv and the Baltic capitals, those drones, en route to hit targets in western Russia, get diverted by Russian electronic jamming and end up entering these countries' territories. In early May, several stray unmanned aircraft crashed in Latvia, one of them damaging an oil storage facility. Those developments triggered a political crisis in Latvia and led to the collapse of its government.

A former member of the German militant group Red Army Faction (RAF) has been jailed for 13 years for carrying out a string of armed robberies between 1999 and 2016. Daniela Klette, 67, was finally caught in a flat in Berlin in 2024 after more than 30 years on the run. She went on trial last year. Her defence had called for her acquittal but the court in Verden in Lower Saxony found her guilty on Wednesday of aggravated robbery, violating weapons laws and other offences over a 17-year period. Klette's RAF group, also known as the Baader-Meinhof gang, was eventually disbanded after a campaign of murder, kidnapping and bombing from the early 1970s to the early 1990s.

The Premier League season might be long-forgotten already - but we're definitely still in the window where bragging about how well you did in fantasy football is just about acceptable. Plenty of people will have been frantically checking the app on Sunday to see if they'd beaten friends, family or colleagues and topped their mini leagues. Someone who was refreshing a little more than most is 23-year-old Everton fan Erik Ibsen. But the Danish medical student managed to hold on to his lead to be crowned the Fantasy Premier League (FPL) champion - in his first season playing the game. Ibsen only started playing because his sister was doing a work league and wanted some help, which turned into him picking his own team for sibling rivalry.

VILNIUS/STOCKHOLM/LONDON - Ukrainian drones have strayed into Baltic countries' airspace in recent weeks, sowing confusion and raising tensions with Russia at a time when U.S. commitment to NATO's collective security is in question. The airspace incursions have occurred as Ukraine, seeking to land heavier blows on Russia four years after Moscow's full-scale invasion, uses exploding drones to hit Russian Baltic ports that handle nearly 40% of national oil and gas exports. In most cases, Kyiv and the Baltic states have confirmed the stray drones are Ukrainian but have blamed Russia for causing them to deviate from their flight path with the use of electronic defenses that jam or spoof signals. In a time of both misinformation and too much information, quality journalism is more crucial than ever. By subscribing, you can help us get the story right.

'My job is going': U.K. workers squeezed out by AI In the U.K., the IMF estimated in 2024 that more than two-thirds of British workers perform tasks that AI could potentially carry out. London - When a client asked her a year ago to design a glossary to train an artificial intelligence system, translator Jessica Spengler realized she was going to train her own replacement. "That was the day I really thought ... my job is going," said the 52-year-old, who translates into English for German educational and historical organizations. In the U.K., where services account for around 80% of the economy, AI has become flexible, fast and inexpensive competition for many white-collar workers, with the impacts beginning to emerge. In a time of both misinformation and too much information, quality journalism is more crucial than ever.

Meet the UK's very own LeBron James... but not as you know it Look out LeBron James and Michael Jordan, there's a new basketball champ around. But it was made in Lisburn rather than Los Angeles or Chicago. The name 25416 may not appear on many replica vests, but it can shoot hoops like no-one else. And the basketball-playing robot won a school in Lisburn first prize at the UK-wide First Tech Challenge robotics competition. The team of sixth-formers from Friends' School came top of 48 schools from across the UK at the competition held in London's Copper Box Arena. Going down and working on it with my friends is honestly one of the highlights of my last year in school, he said.

An ethical hacker who just won major prizes at a prestigious international competition says her days of competing could be numbered due to the rise of AI tools like Claude Mythos. Valentina Palmiotti - better known as Chompie - was the most successful individual at the annual Pwn2Own hacking competition in Berlin. She told BBC News that, for now, AI tools were helping her to win bug bounties - money given to hackers who spot vulnerabilities in online systems before they can be exploited by cyber-criminals. But she said systems like Mythos were so powerful that even champion hackers like her would soon struggle to compete with them. AI has shaken the cyber-security world, with concerns focussing on Mythos in particular.

Lagrangian Relaxation (LR) is a powerful technique for solving large-scale Mixed Integer Linear Programming (MILP), particularly those with decomposable structures, such as vehicle routing or unit commitment problems. By relaxing the coupling constraints, LR enables parallel subproblem solving and often yields tighter dual bounds than standard linear programming relaxations, which is crucial for efficient branch-and-bound pruning. While recent empirical work has shown promising results using machine learning to predict these multipliers, a theoretical understanding of such methods remains an open question. In this work, we bridge this gap by analyzing the problem of learning LR through the lens of Data-driven Algorithm Design, i.e., a statistical learning problem over a distribution of problem instances. Our contributions are as follows: first, we derive a generalization bound of $\mathcal{O}(s^{1.5}/\sqrt{N})$ for the learned multipliers, where $s$ is the number of coupling constraints and $N$ is the sample size. Second, we provide a minimax lower-bound of $Ω(s/\sqrt{N})$, proving that a linear dependency is unavoidable. Third, we constructively close this theoretical gap by proving that Stochastic Gradient Ascent (SGA) with averaging achieves the minimax optimal rate $Θ(s/\sqrt{N})$. Finally, we extend our framework to the learning-to-warm-start setting, proving that it achieves a fast, minimax-optimal rate of $Θ(s/N)$ and establishing a theoretical advantage over direct multiplier prediction.

Understanding the relationship between generalization and privacy remains a central challenge in modern machine learning theory, particularly for deep networks trained by variants of differentially private stochastic gradient descent (DP-SGD). In this work we make progress on this persistent open problem by proving a finite-sample bound on the approximate max-information of DP-SGD that exhibits scaling properties comparable with (Dwork et al, 2015)'s classic result for $ε$-differentially private algorithms, namely at most linear in the dataset size. From our result we obtain a general-purpose PAC-Bayes generalization bound in which the necessary prior distribution can be learned by DP-SGD, as well as a generalization bound for DP-SGD-trained models themselves, with a complexity term that is fully explicit and controlled by the optimization hyperparameters.

Physics-informed machine learning (PIML) integrates mechanistic knowledge, typically in the form of partial differential equations (PDE), into data-driven models. Despite strong empirical performance, its statistical generalisation properties remain poorly understood, particularly in the regression setting with unbounded losses. Existing analyses rely on approximation or stability arguments and do not fully capture how physical structure influences generalisation from finite data. In this work, we develop a PAC-Bayesian framework for PIML that provides high-probability generalisation guarantees in the presence of unbounded losses. We adopt a multi-task perspective that jointly treats data fidelity, PDE residuals, initial and boundary conditions, avoiding the looseness induced by standard union-bound approaches. Our analysis leverages the structure of physics-informed objectives to derive novel bounds where the complexity scales with input-gradient norms of the losses, revealing a direct link between physical regularity and generalisation. We instantiate this framework under Sobolev and Poincaré-type assumptions, yielding two classes of bounds that trade off statistical complexity and smoothness in different regimes. Building on these results, we propose a self-bounding-aware learning algorithm that directly optimises tractable surrogates of the derived bounds, along with a practical procedure to estimate the associated constants in realistic settings. Empirical evaluations on standard PDE benchmarks demonstrate that our bounds are non-vacuous, significantly tighter than union-bound baselines, and can be effectively minimised during training. Overall, our results provide a principled statistical foundation for the generalisation of physics-informed models.