Ties between the US tech giant Palantir and the United Kingdom government are coming under increased scrutiny following the arrest of former UK ambassador to the US Peter Mandelson over his links to the late convicted sex offender Jeffrey Epstein. Despite its public criticism of both Palantir and Mandelson, the UK government has entered into extensive contracts with the US tech giant, signing a defence contract worth 240 million pounds ($323m) in January. The contract was awarded to Palantir directly, while another, worth 330 million pounds ($444m) and involving the UK's Ministry of Health, was awarded in November 2023 following a bidding process. The latter contract's contents, campaigners say, remain heavily redacted . In addition to its role supporting US President Donald Trump's immigration crackdown, which has resulted in killings and unlawful deportations, Palantir has partnered extensively with the Israeli military and its operations in Gaza and the occupied West Bank.

Customer conversations with chatbots can include contact information and personal details that make it easier for scammers to launch phishing attacks and commit fraud.

Two Literal Crypto Bros Built a Real Estate Empire. In 2019, two Canadian brothers blew into Detroit with an irresistible pitch: For $50, almost anyone could become a property owner. When houses decayed and the city intervened, the blame games began. A fire broke out at 10410 Cadieux in March 2025, burning a hole in the roof. The smell hit me first: damp brick, stagnant water, mold, and bleach. I was partway down a flight of wooden stairs that led to the basement of a 1920s duplex in east Detroit, Michigan. Leading the way was Cornell Dorris, a tenant in the building for nearly a decade. Dorris is in his early forties, has two daughters who visit on weekends, and makes a living smoking meat and cooking for events. As my eyes adjusted, I made out rodent droppings and a black puddle that spread across the basement floor. "Anytime it rains, the water comes down," Dorris said. The air was unnaturally heavy, and I felt a nagging urge to leave. Dorris doesn't have a typical landlord. Almost four years ago, his building was acquired by a startup called RealToken, or RealT.

Kernel-based quadrature rules are becoming important in machine learning and statistics, as they achieve super-$¥sqrt{n}$ convergence rates in numerical integration, and thus provide alternatives to Monte Carlo integration in challenging settings where integrands are expensive to evaluate or where integrands are high dimensional. These rules are based on the assumption that the integrand has a certain degree of smoothness, which is expressed as that the integrand belongs to a certain reproducing kernel Hilbert space (RKHS). However, this assumption can be violated in practice (e.g., when the integrand is a black box function), and no general theory has been established for the convergence of kernel quadratures in such misspecified settings. Our contribution is in proving that kernel quadratures can be consistent even when the integrand does not belong to the assumed RKHS, i.e., when the integrand is less smooth than assumed. Specifically, we derive convergence rates that depend on the (unknown) lesser smoothness of the integrand, where the degree of smoothness is expressed via powers of RKHSs or via Sobolev spaces.

America's drone industry lags behind China's dominance, but Congress and Trump's $2.5 billion investment aims to rebuild U.S. military and commercial drone production by 2027.

Ukrainian President Volodymyr Zelensky is set to visit Prime Minister Sir Keir Starmer in the UK on Tuesday to agree a new defence partnership aimed at tackling cheap attack drones. Downing Street said the deal would bring together Ukrainian expertise and the UK's industrial base to manufacture and supply drones and other capabilities. The two leaders are also expected to discuss further support Ukraine against Russia's full-scale invasion, now in its fourth year. Their meeting comes as the US-Israeli war with Iran enters a third week, during which US President Donald Trump has criticised the UK and other countries over the extent of their response to the conflict. Under the partnership between the UK and Ukraine, closer co-operation in the defence industries will also be sought with third countries as part of efforts to bolster international security.

US President Donald Trump has renewed his criticism of the UK government over its response to the Iran conflict, after Prime Minister Sir Keir Starmer said the country would not be drawn into the wider war. Trump told reporters on Monday he was not happy with the UK, adding it should be involved enthusiastically in efforts to reopen the Strait of Hormuz - a vital oil shipping channel . He later told a press conference there were some countries that greatly disappointed me before he singled out the UK, which he said had been considered the Rolls-Royce of allies. Trump's remarks came after Sir Keir said the UK was working with allies on a viable, collective plan to reopen the strait. Sir Keir also said the UK already had minehunters in the region but there was no decision yet on what action would be taken.

We provide two fundamental results on the population (infinite-sample) likelihood function of Gaussian mixture models with $M \geq 3$ components. Our first main result shows that the population likelihood function has bad local maxima even in the special case of equally-weighted mixtures of well-separated and spherical Gaussians. We prove that the log-likelihood value of these bad local maxima can be arbitrarily worse than that of any global optimum, thereby resolving an open question of Srebro (2007). Our second main result shows that the EM algorithm (or a first-order variant of it) with random initialization will converge to bad critical points with probability at least $1-e^{-\Omega(M)}$. We further establish that a first-order variant of EM will not converge to strict saddle points almost surely, indicating that the poor performance of the first-order method can be attributed to the existence of bad local maxima rather than bad saddle points. Overall, our results highlight the necessity of careful initialization when using the EM algorithm in practice, even when applied in highly favorable settings.

We present Cyclades, a general framework for parallelizing stochastic optimization algorithms in a shared memory setting. Cyclades is asynchronous during model updates, and requires no memory locking mechanisms, similar to Hogwild!-type algorithms. Unlike Hogwild!, Cyclades introduces no conflicts during parallel execution, and offers a black-box analysis for provable speedups across a large family of algorithms. Due to its inherent cache locality and conflict-free nature, our multi-core implementation of Cyclades consistently outperforms Hogwild!-type algorithms on sufficiently sparse datasets, leading to up to 40% speedup gains compared to Hogwild!, and up to 5\times gains over asynchronous implementations of variance reduction algorithms.

Graves being prepared for the victims of an airstrike on a school in Minab in southern Iran, 2 March 2026. Graves being prepared for the victims of an airstrike on a school in Minab in southern Iran, 2 March 2026. A photo of Iran's bombed schoolgirl graveyard went around the world. T he graves, freshly dug, lie in neat rows of 20 across. More than 60 have already been carved out of the earth, with a few clusters of people standing gathered around them.