Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Do YOU have one gathering dust in your attic? It's time to feel old - as believe it or not, Pokémon turns 30 today. The franchise continues to sell billions of cards every single year, but a rare handful of highly sought-after cards can be worth thousands, if not millions, at auction.

Discrete diffusion models have achieved strong empirical performance in text and other symbolic domains, with masked (absorbing-rate) variants emerging as competitive alternatives to autoregressive models. Among existing samplers, the Euler method remains the standard choice in many applications, and more recently, the First-Hitting Sampler (FHS) has shown considerable promise for masked diffusion models. Despite their practical success, the theoretical understanding of these samplers remains limited. Existing analyses are conducted in Kullback-Leibler (KL) divergence, which often yields loose parameter dependencies and requires strong assumptions on score estimation. Moreover, these guarantees do not cover recently developed high-performance sampler of FHS. In this work, we first develop a direct total-variation (TV) based analysis for the Euler method that overcomes these limitations. Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees without requiring any surrogate initialization. Also for this setting, we provide the first convergence lower bound for the Euler sampler, establishing tightness with respect to both the data dimension $d$ and the target accuracy $\varepsilon$. Finally, we analyze the FHS sampler and show that it incurs no sampling error beyond that induced by score estimation, which we show to be tight with a matching lower error bound. Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS, which may be of independent interest.

Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Revealed: Unexplained objects that stop and accelerate quickly in space detected by'highly qualified observers, says former UFO chief. 'Spacecraft we know don't behave that way' Sign up for our US Editor's Picks newsletter to get all the best exclusive stories The Pentagon's UFO office former chief has revealed unexplained objects were detected in space - and that some performed maneuvers defying anything in America's known aerospace arsenal. Lieutenant Colonel Tim Phillips, who was acting director of the All-domain Anomaly Resolution Office (AARO) until last April, told the Daily Mail that while most cases involved objects in the air, some detections extended beyond the atmosphere.

Switching to big tech alternatives is easier than you might imagine. Switching to big tech alternatives is easier than you might imagine. T here's not much to love about big tech these days. So many ills can be laid at its door: social media harms, misinformation, polarisation, mining and misuse of personal data, environmental negligence, tax avoidance, the list goes on. Added to which, Silicon Valley's leaders seem all too keen to cosy up to the Trump administration, to shower the president with bribes - sorry, gifts - and remain silent about his worsening political overreach. And that's before we get to the rampant " enshittification ", as the tech writer Cory Doctorow describes it, which means that by design many big tech products have become less useful and more extractive than they were when we originally signed up to them.

ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' A 3.5-magnitude earthquake shook central Kansas on Wednesday, jolting an area layered over ancient volcanic rock deep below the surface. The tremor was detected at 2.14pm local time (3.14pm Although Kansas has no active volcanoes, the region marks the southern reach of the Midcontinent Rift System, a massive tectonic event that nearly split North America apart in Earth's distant past.

Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Emperor penguins are on the pathway to EXTINCTION: Satellite images reveal how shrinking sea ice is forcing birds into crowded groups - with potentially'catastrophic' consequences READ MORE: Antarctica's worst-case climate scenario laid bare Emperor penguins are one of the Antarctic's most iconic animals - but these majestic birds are on the pathway to extinction. For the first time, satellite images have captured the penguins' elusive moulting colonies, where they replace their feathers with new waterproof plumage. Moulting is a particularly dangerous time for emperor penguins as they cannot enter the water to feed for several weeks while their new plumage regrows.

Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Earth's'Doomsday Vault' has been updated: Scientists add 7,800 samples into the secretive bunker in the Arctic A bunker hidden in the Arctic might sound like somewhere a Bond villain would hide out - but the real-life'Doomsday Vault' actually serves a very serious purpose. The Svalbard Global Seed Vault, located beneath a mountain in Spitsbergen, a remote island in the Norwegian archipelago of Svalbard, houses'spare copies' of seeds from around the world. That collection has now been updated with over 7,800 seed varieties, including staple grains from Africa, olives from Spain, and ancient crops from Guatemala.

ROTC students at Old Dominion subdued and killed ISIS-linked gunman who left one dead, two wounded after shouting'Allahu Akbar' and opened fire Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Hollywood icon who starred in Psycho after Hitchcock dubbed her'my new Grace Kelly' looks incredible at 95 Kylie Jenner's total humiliation in Hollywood: Derogatory rumor leaves her boyfriend's peers'laughing at her' behind her back Tucker Carlson erupts at Trump adviser as she hurls'SLANDER' claim linking him to synagogue shooting Ben Affleck'scores $600m deal' with Netflix to sell his AI film start-up Long hair over 45 is ageing and try-hard. I've finally cut mine off. Alexander brothers' alleged HIGH SCHOOL rape video: Classmates speak out on sickening footage... as creepy unseen photos are exposed Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Ey up AI! Scientists are teaching artificial intelligence how to understand UK accents and dialects - so, how many of these regional terms do YOU know? Scientists are teaching AI how to understand slang words such as'chuck' and'nowt' so that automated phone lines can understand local callers. Councils across the UK are turning to artificial intelligence to man their phones, helping people with enquiries such as when to put their bins out or how to pay their council tax.

Horrifying next twist in the Alexander brothers case: MAUREEN CALLAHAN exposes an unthinkable perversion that's been hiding in plain sight Alexander brothers' alleged HIGH SCHOOL gang rape video: Classmates speak out on sick'taking turns' footage... as creepy unseen photos are exposed Model Cindy Crawford, 60, mocked for her'out of touch' morning routine: 'Nothing about this is normal' Kentucky mother and daughter turn down $26.5MILLION to sell their farms to secretive tech giant that wants to build data center there Live Nation executives mocked'stupid' concert-goers in emails where they bragged about how to best rip them off: '$60 for closer grass' NFL superstar Xavier Worthy spills all on Travis Kelce, the Chiefs' struggles... and having Taylor Swift as his No 1 fan Heartbreaking video shows very elderly DoorDash driver shuffle down customer's driveway with coffee order because he is too poor to retire Amber Valletta, 52, was a '90s Vogue model who made movies with Sandra Bullock and Kate Hudson, see her now Nancy Mace throws herself into Iran warzone as she goes rogue on Middle East rescue mission: 'I AM that person' Hidden toxins in kids' treats EXPOSED: Health guru Jillian Michaels' sit-down with Casey DeSantis reveals dangers lurking in popular foods Why are animals picking on Punch the monkey? Scientists have revealed the tragic truth about Punch the monkey - the viral macaque who has stolen the hearts of millions across social media. The seven-month-old Japanese macaque was born at Ichikawa Zoo last year, where he was rejected by his mother. Zookeepers gave him a stuffed orangutan toy, who he quickly formed a bond with - with viral footage showing him clinging to the plushie. Fans were briefly relieved when footage emerged of another macaque grooming and comforting Punch.

Ukraine has responded to a war it didn't start by creating an industry it doesn't want, but could the nation's drone expertise help it rebuild? To learn more, gained exclusive access to the research labs, factories and military training schools behind Ukraine's drones Killhouse Academy, run by the 3rd Assault Brigade, is Ukraine's leading drone-pilot school. The grinding, attritional war between Russia and Ukraine is now entirely dominated by drones. Russia pummels Ukraine with long-range kamikaze aircraft and Ukraine knocks them out of the sky with specialised interceptors. The front line has transitioned from an artillery battle to a first-person-view drone fight, while ground-based robots are increasingly used to deliver ammunition and supplies, launch attacks and evacuate the wounded. As a result, in the four years since Russia's full-scale invasion, Ukraine has created from nothing an entire industry and ecosystem capable of designing, manufacturing and operating a variety of ingenious drones.