This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG . China's robot-run hotel opens to public in 2027 A missing kitten rode under a car hood.

Leaked footage shows astonishing first look INSIDE Taylor Swift and Travis Kelce's wedding: See the bride's aisle, altar and couple's personal touches as A-listers vanish through MSG castle's'magic doors' Taylor Swift's '40-page prenup': How $2BILLION in assets divide up... and the one major concession Travis is predicted to have written in as special clause America's most expensive home gets jaw-dropping $63MILLION price cut... but it will still cost you $125m Huge crowds gather in Tehran for funeral of slain Iranian supreme leader Ali Khamenei as millions call for'revenge' against the US Sorry, but Taylor Swift's wedding was a tacky, childish, narcissistic spectacle of utter trash... now we all know what comes next: MAUREEN CALLAHAN Ryan Reynolds shuns Taylor Swift wedding controversy as he shares support for Canada - amid wife Blake Lively's FURY over snub from former pal's nuptials to Travis Kelce Lena Dunham leaves Taylor Swift wedding guests GASPING with shockingly rude dinner ...

A large-scale clinical trial has shown that even long-term consumption of DHA--an omega-3 fatty acid found in abundance in oily fish--may not lead to improvements in cognitive function. Docosahexaenoic acid (DHA), an omega-3 fatty acid found in abundance in oily fish such as mackerel and sardines, is thought to improve cognitive function by supporting connections between brain cells. However, it has never been conclusively demonstrated that DHA taken as a dietary supplement actually reaches the brain or provides measurable benefits against dementia . Against this backdrop, a research team at the USC School of Medicine has published the results of a large, two-year clinical trial involving older adults at elevated risk of developing Alzheimer's disease . The study found that while high-dose DHA supplements do indeed reach the brain, they did not improve memory or cognitive function, nor did they slow brain atrophy.

Some features are more clinically useful than others. Smartwatches and other wearables have moved far beyond just tracking your steps and heart rate. Many of today's versions can monitor everything from sleep and skin temperature to respiratory rate, blood oxygen, heart rate variability and even alert you to possible signs of sleep apnea . If you took Big Tech's marketing at face value, you might conclude that your smartwatch is on the verge of becoming a real-life Star Trek Tricorder. But how reliable are wearables for spotting early signs of illnesses or other medical conditions?

What could new rights for unmarried couples mean for your money? When Amelia's fiance died suddenly in his 20s, just months before their wedding, she never imagined the legal and financial turmoil that would follow. I lost him, she says, and then I lost everything we'd ever built together. The couple had been together more than seven years and shared a business. But they were not married and Simon did not have a will, so his mother and father inherited all of his assets - apart from the couple's house - and Amelia was unable to stop them.

Parents warned not to publicly share children's images amid AI abuse risks Parents should not publicly post images of their children online due to the growth of AI-generated abuse imagery, the National Crime Agency (NCA) has warned. Along with the Internet Watch Foundation (IWF), it said there is a growing threat of children's images online being used to create child sexual abuse material (CSAM). More than 8,000 AI-generated images and videos of realistic child sexual abuse were identified by the IWF in 2025, it said - adding this was a 14% increase on the year before. While we and policing colleagues tackle offenders, prevention remains vital, said Tim Wright, a senior manager at the NCA. In partnership with the IWF, the organisation has released fresh guidance for parents outlining steps they can take to help keep their children safe online.

This material may not be published, broadcast, rewritten, or redistributed. Quotes displayed in real-time or delayed by at least 15 minutes. Market data provided by Factset . Powered and implemented by FactSet Digital Solutions . Mutual Fund and ETF data provided by LSEG .

For training-data-based model risk prediction, $K$-fold cross-validation~(CV) is widely used to mitigate the well-known over-optimism of the empirical risk and is often regarded as reliable. However, for binary classification via empirical risk minimization, our numerical studies reveal a surprising phenomenon: $K$-fold CV may perform poorly in estimating class-specific risks, even worse than the empirical estimator. We perform a higher-order asymptotic analysis showing that $K$-fold CV may converge at a slower rate, whereas the empirical estimator exhibits a second-order asymptotic bias that explains its over-optimism. These findings motivate a novel two-step procedure for model risk prediction, termed cross-audit projection (CAP). The cross-audit step adopts the same resampling scheme as $K$-fold CV to estimate over-optimism in subsamples, while the asymptotic-theory-informed projection step adjusts for the reduced sample size in bias correction of the empirical risk. The resulting CAP estimator is first-order asymptotically equivalent to the empirical risk while achieving second-order asymptotic unbiasedness. An accompanying inference procedure is also developed. Simulation studies support theoretical advantages of CAP and demonstrate favorable finite-sample performance. An application to breast cancer detection further illustrates the proposed method.

Evaluations of LLM personas via psychometric questionnaires typically rely on aggregate scores, discarding within-instance correlation structure. We test whether this geometric structure is intrinsic or frame-dependent. Constructing within-instance correlation matrices from IPIP-50 responses, we analyze geometry on SPD manifolds under manipulated question orderings in GPT-4o simulating American and Chinese-American personas. We find that persona expression comprises two dissociable components: aggregated features (Big Five scores) degrade under randomization (21% drop) but are frame-robust; geometric features (SPD manifold) collapse under frame misalignment (42% drop) but recover substantially (to 84%) under shared frames, surpassing aggregated features (76%). This collapse-recovery pattern reveals that persona geometry is not intrinsic but a frame-dependent coordination pattern encoding information invisible to aggregation. Our findings establish a dual-nature framework for LLM personas, frame-dependent geometry versus frame-robust aggregates, necessitating frame-aware evaluation and challenging static trait conceptions.

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