Survival analysis encompasses a broad range of methods for analyzing time-to-event data, with one key objective being the comparison of survival curves across groups. Traditional approaches for identifying clusters of survival curves often rely on computationally intensive bootstrap techniques to approximate the null hypothesis distribution. While effective, these methods impose significant computational burdens. In this work, we propose a novel approach that leverages the k-means and log-rank test to efficiently identify and cluster survival curves. Our method eliminates the need for computationally expensive resampling, significantly reducing processing time while maintaining statistical reliability. By systematically evaluating survival curves and determining optimal clusters, the proposed method ensures a practical and scalable alternative for large-scale survival data analysis. Through simulation studies, we demonstrate that our approach achieves results comparable to existing bootstrap-based clustering methods while dramatically improving computational efficiency. These findings suggest that the log-rank-based clustering procedure offers a viable and time-efficient solution for researchers working with multiple survival curves in medical and epidemiological studies.

Streamflow forecasting is crucial for water resource management and risk mitigation. While deep learning models have achieved strong predictive performance, they often overlook underlying physical processes, limiting interpretability and generalization. Recent causal learning approaches address these issues by integrating domain knowledge, yet they typically rely on fixed causal graphs that fail to adapt to data. We propose CauStream, a unified framework for causal spatiotemporal streamflow forecasting. CauSTream jointly learns (i) a runoff causal graph among meteorological forcings and (ii) a routing graph capturing dynamic dependencies across stations. We further establish identifiability conditions for these causal structures under a nonparametric setting. We evaluate CauSTream on three major U.S. river basins across three forecasting horizons. The model consistently outperforms prior state-of-the-art methods, with performance gaps widening at longer forecast windows, indicating stronger generalization to unseen conditions. Beyond forecasting, CauSTream also learns causal graphs that capture relationships among hydrological factors and stations. The inferred structures align closely with established domain knowledge, offering interpretable insights into watershed dynamics. CauSTream offers a principled foundation for causal spatiotemporal modeling, with the potential to extend to a wide range of scientific and environmental applications.

Instacart settles Federal Trade Commission's claim it deceived US shoppers Instacart has agreed to pay $60m in refunds to settle allegations brought by the United States Federal Trade Commission (FTC) that the online grocery delivery platform deceived consumers about its membership programme and free delivery offers. According to court documents filed in San Francisco on Thursday, Instacart's offer of "free delivery" for first orders was illusory because shoppers were charged other fees, the FTC alleged. "The FTC is focused on monitoring online delivery services to ensure that competitors are transparently competing on price and delivery terms," said Christopher Mufarrige, who leads the FTC's consumer protection work. An Instacart spokesperson said the company flatly denies any allegations of wrongdoing, but that the settlement allows the company to focus on shoppers and retailers. "We provide straightforward marketing, transparent pricing and fees, clear terms, easy cancellation, and generous refund policies -- all in full compliance with the law and exceeding industry norms," the spokesperson said.

Has Trump failed to sell the Iran war to the world? Are US-Israeli attacks against Iran legal? Why did Trump fire Kristi Noem as DHS secretary? United States President Donald Trump is getting into the fusion power business through a $6bn merger of his social media firm and Google-backed TAE Technologies, just days after industry representatives urged federal funding. The all-stock deal, announced on Thursday, is an ambitious bet on the power boom spurred by artificial intelligence (AI) data centres and adds to the Trump family's growing roster of diverse ventures from cryptocurrency to real estate holdings and mobile services.

The UK government says it will ban so-called nudification apps as part of efforts to tackle misogyny online. New laws - announced on Thursday as part of a wider strategy to halve violence against women and girls - will make it illegal to create and supply AI tools letting users edit images to seemingly remove someone's clothing. The new offences would build on existing rules around sexually explicit deepfakes and intimate image abuse, the government said. Women and girls deserve to be safe online as well as offline, said Technology Secretary Liz Kendall. We will not stand by while technology is weaponised to abuse, humiliate and exploit them through the creation of non-consensual sexually explicit deepfakes.

A husband and wife have died after being trapped in a private sauna room that caught fire in Japan on Monday. Tokyo police are investigating whether a faulty doorknob trapped the couple inside the room at Sauna Tiger, in the city's Akasaka district, local media has reported. Investigators also found that the facility's emergency alarm system was switched off, and allegedly had been for two years. We offer our deepest condolences... and our heartfelt sympathies for the deep grief and pain that cannot be expressed in words, Sauna Tiger said in a statement on its website. The victims have been named by local media as Yoko Matsuda, a 37-year-old nail artist, and her husband Masanari, 36, who ran a beauty salon.

Inside the former US embassy that's now one of the world's top luxury hotels - with 8 bars and restaurants and suites to book for £26,100 The world's most expensive cities for days out revealed, with London in the top 15 Going beyond the guidebook: Here are 10 must-try cultural and wildlife experiences in Australia's'Garden State' Fairy-tale villages, castle tours and dinner at Austria's oldest winery: These enchanting river cruises will take you to the heart of each picturesque port of call you visit Revealed: The world's best new luxury hotel is in the UK - and it has a huge pool and rooftop bar Travel expert reveals the'science-backed tool' to help overcome fear of flying Eurostar's'snow train' set to return this week for winter Could YOU pass France's new'civic examination' needed to live in the country? Try these sample questions and find out... Airline finds'lost' Boeing 737 a decade after it vanished'If you don't enjoy Benidorm, you've only got yourself to blame': Meet the British couple who have been to the Spanish hotspot more than 100 TIMES The'dangerous' destinations that are actually not scary - and why you should holiday there next Brit who moved to the world's most desirable place to live reveals the soaring unexpected costs of relocating A major UK city is set to get driverless trains next year as part of its rail modernisation project. In 2023, new trains were launched in Glasgow as part of the full-scale upgrade to improve the city's subway after more than 30 years. The renovations have continued and now, the Strathclyde Partnership for Transport (SPT) has announced Unattended Train Operation will be introduced to Glasgow. The modernisation project is in its'final stages,' Time Out reports, and the driverless subway trains are expected to be brought in next year.

Major cities across Sudan, including the capital, Khartoum, and coastal city Port Sudan, have been plunged into darkness after drone strikes hit a key power plant in the country's east. Flames and smoke rose from the facility in Atbara, River Nile state on Thursday, which is controlled by the government-aligned Sudanese Armed Forces (SAF) and under attack by the paramilitary Rapid Support Forces (RSF) in the ongoing civil war that has ripped the nation apart. Sudan's RSF trying to hide atrocities: Report Two civil defence members were killed, power plant officials said, while trying to extinguish the fire that erupted after the first strike, adding that rescue workers were injured when a second drone hit as they battled the flames. Al Jazeera correspondent Mohamed Vall in Port Sudan reported that residents initially thought a routine power cut had occurred, only to learn it was linked to incidents in Atbara, roughly 320km (about 230 miles) north of Khartoum. He added that such strikes have become a frequent occurrence in Sudan's war.

Kimberly Guilfoyle's bitter reaction to Don Jr's engagement with Bettina Anderson as scorned ex insists she'wants what's best' for the first son Simone Biles is slammed by furious animal rights activists after allegedly chopping her dog's EARS off The full story of Nick Reiner and these murders is so much more unbearable than everyone thinks. Even Hollywood wouldn't dare write it: MAUREEN CALLAHAN I sneakily looked at my perfect son's phone... What a terrible mistake! Rob Reiner and his wife's cause of death revealed'It was a cover up': Kirsty MacColl's ex-husband speaks out 25 years on from Fairytale of New York singer's death... and says she was'killed by speedboat driven by the richest man in Mexico' Reiner family bombshell as insiders reveal who is paying for Nick's celebrity lawyer... their secret motive... and who will REALLY inherit $200m fortune Trump's border patrol boss gets in VERY public spat with city mayor as he gives him rude awakening Chilling new video of Nick Reiner making disturbing comments about murder... as friend reveals dad Rob's tragic failed attempt to save him: 'I'm going to kill that f***ing dog' Tara Reid speaks out for the first time since THAT video emerged... and tells KATIE HIND why she is convinced she was spiked after watching CCTV How Bettina Anderson's engagement ring measures up to Kimberly Guilfoyle's... and which Don Jr spent most money on Elon Musk is blasted on social media over'pathetic' comments about Sydney Sweeney's breasts Biohacker Bryan Johnson says he will be immortal in 15 years... as he finally'cracks' the secret to living forever Natalee Holloway's killer Joran van der Sloot attempts to take his own life inside maximum-security Peruvian prison Chilling new details of father's death a day before facing justice for leaving his daughter, 2, to die in a hot car Pouty dine-and-dash diva interrupts judge MULTIPLE times as she's hauled to court for bill-skipping spree Sign up for our US Editor's Picks newsletter to get all the biggest exclusive stories A small town sheriff has admitted he is perplexed by a series of mysterious flying objects which have been bewildering locals in his Wyoming community for more than a year. Unidentified flying objects [ UFOs ] have been regularly spotted for 13 months above the Jim Bridger Power Plant and Sweetwater County's Red Desert. John Grossnickle, the Sheriff of Sweetwater County, saw lit-up, drone-like objects as recently as December 13, his spokesman Jason Mower told Cowboy State Daily .

The exhibition is scheduled to continue through Friday. Rapidus, Japan's government-backed semiconductor developer, is betting on artificial intelligence-enhanced design tools to give it an edge over its competitors, in an effort to speed up its chip-design process and minimize costs. The firm made the announcement during Semicon, a semiconductor-industry event being held in Tokyo from Wednesday to Friday at the Tokyo Big Sight convention center. Rapidus' newly announced suite of offerings, which will be rolled out next year, includes Raads Generator, an AI-assisted design tool modeled on large-scale language models -- AI systems trained on datasets -- and optimized for 2-nanometer chip manufacturing. In a time of both misinformation and too much information, quality journalism is more crucial than ever.