Is Trump losing patience with Putin? Will sanctions against Russian oil giants hurt Putin? Is the fall of Pokrovsk, Ukraine's key eastern stronghold, inevitable? Pokrovsk, a key fortress and logistical hub for Ukrainian forces in the eastern region of Donbas, has been under siege for almost two years. But in recent weeks, tens of thousands of Russian soldiers have been storming the town around the clock, taking over the streets where buildings are mostly reduced to bombed-out, deserted ruins. They use reconnaissance drones and satellite images to identify gaps in Ukrainian defences and use tiny groups of soldiers who are attacked and killed in droves by Ukrainian drones .

At seventy-three, the former front man of Talking Heads is still asking questions about what it means to be alive. "When you step onstage, it's a very artificial situation," Byrne said. "To pretend it's not--that isn't being authentic." If you spend enough time wandering around downtown Manhattan, the odds are that you'll eventually encounter the musician David Byrne riding a bicycle. One day this past June, pedalling alongside Byrne from his apartment in Chelsea to the Governors Island ferry, I watched at least a dozen New Yorkers clock his profile, whipping around to squint, softly pinching the arm of their companion and whispering, "Was that . . . By then, Byrne was gone, a tuft of white hair whizzing toward the horizon. Spotting Byrne on two wheels has become a New York City rite of passage, like sussing out the best halal cart in midtown, or dropping something important onto the subway tracks. During the few months that Byrne and I spent together, I never saw him traverse the ...

Palantir's CEO is good with ICE and says he defends human rights. But will Israel and Trump ever go too far for him? Alex Karp and I would not seem to have much in common. I work for WIRED, which does tough reporting on Trumpworld; Karp is the CEO of Palantir, a $450 billion firm that has contracts with agencies like the CIA and ICE and worked for the Israeli military during its campaign in Gaza. I live in the East Village of New York City, and the home Karp spends the most time in is a 500-acre compound in rural New Hampshire. I was a plain old English major, and he's got a law degree and a PhD in philosophy, studying under the legendary Jürgen Habermas. I consider myself a progressive; Karp regards that stuff as "pagan religion." But we can bond over one shared status: Both of us are alumni of Central High School, a Philadelphia magnet school. I have some years on the 58-year-old executive.)

Stocks from the United States to Japan have risen sharply amid hopes that an end to the longest US government shutdown in history is imminent. US lawmakers on Sunday moved to end a five-week impasse over government funding, a boost for investors unnerved by signs of growing weakness in the US economy and the sky-high evaluations of firms involved in artificial intelligence. The funding package still needs to win final approval in the Senate and then pass the US House of Representatives, after which it would go to US President Donald Trump for his signature - a process expected to take days. Stock markets in the Asia Pacific made large gains on Monday, while futures in the US also rose in advance of stock exchanges reopening. South Korea's benchmark KOSPI led the gains, rising about 3 percent as of 4pm local time (07:00 GMT).

Doctors from Scotland and the US have completed what is thought to be a world-first stroke procedure using a robot. Prof Iris Grunwald, of the University of Dundee, performed the remote thrombectomy - the removal of blood clots after a stroke - on a human cadaver that had been donated to medical science. The professor was at Ninewells Hospital in Dundee, while the body she was operating on while using the machine was across the city at the university. Hours later, Ricardo Hanel - a neurosurgeon in Florida - used the technology to carry out the first transatlantic surgery from his Jacksonville base on a human body in Dundee over 4,000 miles (6,400km) away. The team has called it a potential game changer if it becomes approved for use on patients.

A woman who was plunged into sudden menopause after surgery to remove both ovaries is spearheading efforts to change NHS policy. Kate Dyson, 44, from Hastings, East Sussex, underwent the surgery six months ago after having a subtotal hysterectomy in 2021 to remove her uterus - a procedure which leaves the cervix in place. The mum-of-three says she was completely unprepared for the impact of surgical menopause, which is triggered by both ovaries being removed. Honestly, it was like falling off a hormonal cliff edge, she told BBC Radio Sussex. Within hours of the surgery I was home the same day.

You probably don't give much thought to the device that you're reading this article on, as long as it looks good and keeps working. But the elements that power and run it are the subject of an escalating struggle between the world's two biggest economies - the US and China - with African countries in the eye of the storm. The African continent is rich in critical minerals and metals - like lithium, rare earths, cobalt and tungsten - which are vital to making and running our personal tech. Such materials are also essential for everything from electric vehicles, to AI data centres, and weapon systems. China has long been the biggest player in the global market for critical minerals and metals.

Both perspectives are useful in practice: parametric inference estimates the tensor of distributional parameters as a whole, while multiway analysis yields its latent factors for interpretation [1]. Both tasks rely fundamentally on tensor decompositions to represent and exploit underlying structure. However, computing tensor decompositions is notoriously difficult. Degeneracy phenomena lead to non-unique or ill-conditioned factorizations [2] and many tensor problems are NP-hard [3], making even approximate computation intractable in general. These issues put into question the reliability of existing tensor-based inference methods. They are particularly pronounced for the canonical polyadic (CP) decomposition [2], which, despite its widespread use, lacks the theoretical guarantees enjoyed by other tensor formats. Computing CP factors, i.e., multiway analysis, with minimal variance across multiple sets of observations would enhance the reliability of multiway analysis and parametric inference, offering practitioners more confidence in their results while reducing the need for extensive data collection. 1

As predictive algorithms grow in popularity, using the same dataset to both train and test a new model has become routine across research, policy, and industry. Sample-splitting attains valid inference on model properties by using separate subsamples to estimate the model and to evaluate it. However, this approach has two drawbacks, since each task uses only part of the data, and different splits can lead to widely different estimates. Averaging across multiple splits, I develop an inference approach that uses more data for training, uses the entire sample for testing, and improves reproducibility. I address the statistical dependence from reusing observations across splits by proving a new central limit theorem for a large class of split-sample estimators under arguably mild and general conditions. Importantly, I make no restrictions on model complexity or convergence rates. I show that confidence intervals based on the normal approximation are valid for many applications, but may undercover in important cases of interest, such as comparing the performance between two models. I develop a new inference approach for such cases, explicitly accounting for the dependence across splits. Moreover, I provide a measure of reproducibility for p-values obtained from split-sample estimators. Finally, I apply my results to two important problems in development and public economics: predicting poverty and learning heterogeneous treatment effects in randomized experiments. I show that my inference approach with repeated cross-fitting achieves better power than previous alternatives, often enough to find statistical significance that would otherwise be missed.

We establish parameter inference for the Poisson canonical polyadic (PCP) tensor model through a latent-variable formulation. Our approach exploits the observation that any random PCP tensor can be derived by marginalizing an unobservable random tensor of one dimension larger. The loglikelihood of this larger dimensional tensor, referred to as the "complete" loglikelihood, is comprised of multiple rank one PCP loglikelihoods. Using this methodology, we first derive non-iterative maximum likelihood estimators for the PCP model and demonstrate that several existing algorithms for fitting non-negative matrix and tensor factorizations are Expectation-Maximization algorithms. Next, we derive the observed and expected Fisher information matrices for the PCP model. The Fisher information provides us crucial insights into the well-posedness of the tensor model, such as the role that tensor rank plays in identifiability and indeterminacy. For the special case of rank one PCP models, we demonstrate that these results are greatly simplified.