We study the problem of estimating the arrival times of vertices in a uniform random recursive tree from its unlabeled structure. We adopt a pointwise perspective and analyze the distribution of the relative estimation error, and derive tail bounds that are uniform in both the vertex and the tree size. For the ranking induced by Jordan centrality, the probability that the estimate exceeds the true arrival time by a factor $S$ decays on the order of $1/S$, while the probability of underestimating the arrival time by a factor $1/S$ decays exponentially in $S$. We introduce a refined centrality measure whose overestimation tail decays on the order of $(\log S)/S^{2}$, at the cost of a heavier lower tail of order $1/S^{2}$. These results reveal a tradeoff between upper- and lower-tail performance in arrival-time estimation that is invisible to the previously studied risk functional. Nevertheless, the refined centrality measure attains the optimal order of the risk for all its parameter values.

Data augmentation is a simple and model-agnostic approach for exploiting known invariances in learning problems. Given a group acting on the input space, one augments the training set with transformed copies of each sample. Because it exploits symmetries without modifying the underlying learning algorithm, data augmentation can be applied broadly across learning methods. However, this universality comes at a computational cost: when the group is large, full group-sized augmentation quickly becomes computationally infeasible. This raises a fundamental question: Can partial data augmentation achieve the same statistical benefits as full augmentation in terms of generalization and sample complexity? We develop a general framework for investigating this question using Fourier analysis and the representation theory of finite groups. We show that, for a broad class of classical learning problems, partial data augmentation based on a randomly sampled subset of group elements achieves the same minimax rates as full augmentation, up to an approximation error that vanishes as the subset size increases. Our results provide a theoretical explanation for why partial augmentation can retain the statistical benefits of full augmentation despite enforcing symmetry only approximately, and shed light on a recently raised question in learning with symmetries: whether statistically optimal learning under general group invariances can be achieved using computationally scalable methods. Moreover, we prove a complementary impossibility result: enforcing exact invariance via data augmentation requires averaging over the entire group, and cannot be achieved by any strict subset when the hypothesis space is sufficiently expressive. Together, these results provide a unified perspective on full and partial data augmentation, as well as exact and approximate symmetry enforcement.

AI-assisted interviews promise to reduce respondent burden in surveys by allowing respondents to describe experiences naturally while an AI system noisily maps those accounts into structured survey variables. That mapping is a measurement process that is fallible, versioned, adaptive, and potentially behaves differently across subgroups. This paper proposes Adaptive Matrix Validation (AMV), a design in which each respondent completes an AI-assisted interview, which is then mapped into tabular data by the AI. Respondents are also asked a small, randomized set of structured questions, which are used for statistical adjustment. The estimator first calibrates the mapped values using validation answers from other respondents, then corrects the remaining error with the validation answers observed for the target respondent. The paper develops estimators for item means, subgroup estimates, and regression coefficients when outcomes, predictors, or both are mapped from interviews. It also gives planning formulas the number of validation questions required and the sample size. A design-calibration simulation, an American Time Use Survey emulation, and a CHAMPS verbal-autopsy narrative study show when sparse validation can improve precision and when it cannot

Russia’s “Project 2026” wasn’t just to spread misinformation on social media — its main goal to create an alternative information ecosystem.

Superhuman announced that it has acquired GPTZero. This AI identification business offers services such as hallucination and plagiarism detection as well as a nifty little tool that displays how much of the internet is artificial intelligence. Superhuman said it plans to integrate GPTZero into its Superhuman Go AI assistant to improve the reach of its existing efforts around AI and authenticity. Teachers and students will still be the priority audience for Superhuman following the acquisition. For its part, GPTZero emphasized that Superhuman would also help put its tools in places where people were already reading and writing.

Ten years on, Brexit's economic impact is becoming clearer Not long after the UK left the EU in 2020, a Bristol-based firm called Eskimo started selling a new kind of high-fashion and energy-efficient electric radiator, based on new technology developed by academics in the city. They planned to send them around Europe using the Channel Tunnel. It was a timely product given Europe's green ambitions, and with orders flowing, its Birmingham factory was being kept busy. The boss Phil Ward tells me his start-up has continued to grow, but that in his view it could have been so much more without what he calls the Long Brexit effect: in 2020, 40% of his exports went to the European Union, and by 2025 it was just 5%. The post-Brexit deal agreed with the EU by then-Prime Minister Boris Johnson in December 2020 guaranteed zero tariffs on exports to the EU, but Ward says that despite this, red tape and paperwork not directly related to tariffs were enough to create delays, costs and the expectation of hassle for prospective customers.

US Olympic legend Bode Miller's alleged illegal drug stash revealed after he was arrested just days before anniversary of daughter's tragic death Trump's inner circle reveal his true feeling on JD Vance... and why the succession war with Rubio is already won: MARK HALPERIN My girlfriend's cuckolding fetish is getting out of hand... Dr. Fauci is subpoenaed after refusing to testify on COVID origins Noah Presgrove's friends hire famous attorney to battle lawsuit claiming teenager was'beat to death' by someone he knew... as fight between'jealous love rivals' emerges Joe Manganiello reveals secret life-threatening health battle which resulted in'amputation' 'Frankenstein' rabbits with tentacles sprouting from their heads invade several US states AMANDA PLATELL: Why Kate must stand firm and protect her family from Sussexes' manipulation - and most of all, her children Shania Twain, 60, slammed for failing to dress age'appropriate' as she hits the stage in VERY racy look Trump's press secretary joins him on Pennsylvania campaign trip less than two months after birth of daughter Vivi Beloved grandma unmasked as killer of autistic granddaughter and second female family member in horror execution-style double murder... as haunting Mother's Day post emerges Dietitians urge caution over'nature's Ozempic' as people take desperate measures to lose weight Aching joints, exhausted, suffering from brain fog... it might not be the menopause says DR PHILIPPA KAYE READ MORE: Scientists blame mothers for Britain's decline in religiosity Religious rituals are practised all around the world - and experts may now know why they're so popular. Researchers have discovered that taking part in ceremonies like baptisms and bat mitzvahs appears to trigger the release of opioids in the brain. These chemicals have been linked to feelings of pain relief, reward and pleasure. They are also released when people take drugs like heroin, morphine and prescription painkillers, producing the'high' that many associate with the experience. The researchers said their findings support the theory that religious rituals evolved as a way for large groups of people to bond.

Things to Do in L.A. Tap to enable a layout that focuses on the article. Fifth grade students work on computers at their South Los Angeles school in 2019. This is read by an automated voice. Please report any issues or inconsistencies here . Los Angeles Unified will ban classroom screen time in preschool through first grade and sharply limit it for older students.

China beats U.S. with world's fastest supercomputer, but race not geared for AI work Workers at Elon Musk's xAI facility, which houses a large supercomputer known as Colossus, used for Artificial Intelligence (AI) data processing, in Memphis, Tennessee, on Sept. 11, 2025 | REUTERS SAN FRANCISCO - China has overtaken the U.S. to win the top spot on a list of the world's fastest supercomputers, but the results may say more about Beijing's desire to show self-sufficiency in computing systems than its standing in the global AI race, experts said. The LineShine system at the National Supercomputing Center in Shenzhen, China, uses domestically designed chips and won the top spot on the TOP500, a biannual global ranking of supercomputers, with the country's first listing in three years. The ranking comes as the U.S. and China are increasingly competing in advanced computing, with U.S. President Donald Trump on Monday signing an executive order that aims to put the U.S. ahead of China in the emerging field of quantum computing. In the June 2026 edition of TOP500, LineShine beat out the previous titleholder, El Capitan, a supercomputer housed at Lawrence Livermore National Laboratory that the U.S. government uses to develop and maintain its nuclear weapons stockpile. But technology and policy experts said the results do not mean that China has the world's fastest computer for AI work because of changes in the computing industry in recent years and the methods used to compile the list.

The world's oldest football has travelled from Stirling to Florida to make an appearance at Scotland's crunch World Cup match against Brazil. The ball, which is believed to date from between 1540 and 1570 was discovered in the 1970s, lodged in the rafters behind the Queen's Chamber at Stirling Castle. It will be displayed at the Coral Gables Museum in Florida until Saturday as well as being shown at the Scotland match on Wednesday . The ball has been loaned to the museum by Stirling Smith Art Gallery and Museum, where it is the prize exhibit in a collection of more than 40,000 items. The ball, which is recognised by Guinness World Records as the world's oldest, external, is roughly the size of a small melon.