Best Power Banks Best Smart Rings Routers vs. Modems Choose the Right Laptop Smart Sprinklers Deals Delivered But This Is Why It's Heartbreaking Designed by Jony Ive and a host of ex-Cupertino colleagues, the Luce shows us what might have been had Apple made good on its $10 billion bet. You know things are bad when the Pope gets involved . No doubt reeling from a launch that somehow went down even worse than Ferrari itself anticipated, the Italian carmaker sought to get the endorsement of none other than His Holiness Pope Leo XIV for its first EV, the Luce. Guided by Ferrari chairman John Elkann and senior Ferrari executives, in a hillside town about 15 miles southeast of Rome, the pontiff sat in the driver's seat and listened patiently as test driver Raffaele De Simone explained the vehicle's controls and driving modes as if he really was speaking to a man clearly in the market for a 1,000-horsepower electric car capable of hitting 62 mph in 2.5 seconds. Meanwhile, as Pope Leo was no doubt pondering how the Luce could boast one of the largest batteries in any production EV yet still only manage a maximum 329 miles, or how an accelerometer on the rear axle somehow worked like a guitar pickup to create in-cabin sound like an "instrument," the market was speaking.

Andy Burnham has accused former Labour Prime Minister Sir Tony Blair of failing to understand what's going on in people's lives and underestimating the impact of inequality. Sir Tony used a 5,600 word essay to argue the Labour government had no coherent plan for the country and had introduced policies that had held back business. He urged Labour not to move to the left and to embrace the radical centre instead. But Burnham, who is widely expected to challenge Sir Keir Starmer for the Labour leadership if he wins a by-election next month, told the Observer Sir Tony doesn't mention inequality once in his critique of where the Labour government has gone wrong. If you don't get how that's driving politics now, if you are not rooting your analysis in the fact that people are unable to live and that things that were taken for granted are no longer affordable, then you are not understanding what's going on, said the mayor of Greater Manchester.

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.