Female pastor is suspended after her shocking Epstein link is exposed... as she compares herself to JESUS while defending their relationship'Tell me to my face': Republican senator torches Noem's replacement as their vicious personal feud spills into public Outrageous full story of scandalous affair that's the talk of Manhattan's exclusive private schools: Family insiders reveal humiliating sex secrets... shock'confession' letter... and the furious relative who exposed it all Ugly new Nicole Kidman and Keith Urban divorce fight ERUPTS: Her friends share humiliating details of'midlife crisis'... and reveal brutal REAL reason daughter Sunday Rose'snubbed' him Perfect All-American family lived in stunning $1.1m Colorado mansion and bankrolled glamorous daughter's horse stables... now matriarch has sullied their good name with a HUGE scandal Meghan unveils new As Ever line with Lilibet... amid claims Netflix has been left with huge $10m surplus of her unsold products after'split' with streamer Woke Democrat, 26, who can't get out of bed in time for meetings loses primary to professor accused of inappropriate relationship by former student I watched the children's book author who poisoned her husband from 5ft away. This is the off-camera moment her mask finally slipped... it was truly chilling I ran America's only Supermax jail: What history's most notorious terrorists and serial killers told me as they waited to die Sinister truth about explosive resignation of Trump's top counter-terror chief Joe Kent... and his shock claim Israel is manipulating the president: MARK HALPERIN Hairdresser who weighs 300lbs says Southwest airport check-in worker looked him up and down and told him he'd have to buy extra seat Kim Kardashian takes a VERY dramatic tumble in towering $80 'stripper heels' and accidentally grabs an'old lady' as she falls on her way out of Vanity Fair Oscar party Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with Saudi, UAE and Qatar energy facilities are evacuated after Iran threatens'full scale economic war' as oil price jumps 5%: Live updates New PILL for psoriasis approved... giving hope to millions suffering from debilitating skin condition How I lost 8st in my 50s and now finally have the figure of my dreams. I've been large my whole life, but I now feel happier than I ever did in my 20s. New York City's accent is dying out, study finds It's something that's fixed from roughly the age of 14. But your accent could be hindering your job prospects, according to a new study.

A US physicist and a Canadian computer scientist have won this year's Turing Award for their invention of a form of seemingly unbreakable encryption. Charles H Bennett and Gilles Brassard's work, which dates back to 1984, is known as quantum cryptography and has redefined secure communication and computing, the award's body said. Scientists believe their work will be central to electronic communications in a world that depends heavily on data-sharing, but which for years has been trying to develop more powerful quantum computers. The Turing Award, named after the mathematician and code-breaker Alan Turing, is known as the Nobel Prize of computing. It comes with a $1m (£800,000) prize.

Meghan unveils new As Ever line with Lilibet... amid claims Netflix has been left with huge $10m surplus of her unsold products after'split' with streamer Outrageous full story of scandalous affair that's the talk of Manhattan's exclusive private schools: Family insiders reveal humiliating sex secrets... shock'confession' letter... and the furious relative who exposed it all Sinister truth about explosive resignation of Trump's top counter-terror chief Joe Kent... and his shock claim Israel is manipulating the president: MARK HALPERIN Ugly new Nicole Kidman and Keith Urban divorce fight ERUPTS: Her friends share humiliating details of'midlife crisis'... and reveal brutal REAL reason daughter Sunday Rose'snubbed' him Kim Kardashian takes a VERY dramatic tumble in towering $80 'stripper heels' and accidentally grabs an'old lady' as she falls on her way out of Vanity Fair Oscars party USA baseball stars slammed over'disgraceful' national anthem gesture before WBC final vs Venezuela Israel says Iran's intelligence chief has been killed in overnight airstrike in latest attack on regime: Live updates Canada's ultimate revenge on Trump over tariffs gathers pace I ran America's only Supermax jail: What history's most notorious terrorists and serial killers told me as they waited to die Fox News anchor issues blistering takedown of liberal media's delusional take on Iran: 'A stalemate? How I lost 8st in my 50s and now finally have the figure of my dreams. I've been large my whole life, but I now feel happier than I ever did in my 20s. Presidential hopeful JB Pritzker's bold defiant bet against black caucus pays off Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with Mamdani forces New York beloved preschool to hike annual fee to $36,000... and parents are fuming Heath Ledger's lookalike daughter Matilda steps out days after 17 year anniversary of late actor's Oscar win Supreme Court's top judge issues chilling warning as Trump targets his own appointees Robot goes BERSERK at a restaurant in California as desperate staff try to drag it away from customers - as one viewer asks'why isn't there a big red power off button?' This is the shocking moment a dancing robot goes berserk at a restaurant, sending food flying while staff try to drag it away.

In a world of plastic water filter pitchers, I tested two of the new generation of stainless-steel filter systems. I will admit that the popularity of those giant, stainless steel, gravity-fed water filters remained a mystery to me for some years--even as multi-gallon water filter systems from brands like British Berkefeld and Berkey seemed to proliferate equally among lovers of doomsday prepping and holistic wellness retreats. I have been testing much different breeds of water filters for more than a year now, including reverse osmosis filters and water pitchers. But often, the big water filter tanks have seemed as much like status symbols as functional items. If you see a big gravity-fed filter, you know the person in question is serious about wellness, survival, or both. What changed my mind about these big stainless steel filters was microplastics . Most water filter pitchers are made of BPA-free plastic. But as new research shows that bottled-water drinkers ingest tens of thousands of excess microplastic particles, wellness lovers have begun to look askance at water filters that are themselves made of plastic.

Meghan unveils new As Ever line with Lilibet... amid claims Netflix has been left with huge $10m surplus of her unsold products amid'split' with streamer Outrageous full story of scandalous affair that's the talk of Manhattan's exclusive private schools: Family insiders reveal humiliating sex secrets... shock'confession' letter... and the furious relative who exposed it all Sinister truth about explosive resignation of Trump's top counter-terror chief Joe Kent... and his shock claim Israel is manipulating the president: MARK HALPERIN Canada's ultimate revenge on Trump over tariffs gathers pace Ugly new Nicole Kidman and Keith Urban divorce fight ERUPTS: Her friends share humiliating details of'midlife crisis'... and reveal brutal REAL reason daughter Sunday Rose'snubbed' him Kim Kardashian takes a VERY dramatic tumble in towering $80 'stripper heels' and accidentally grabs an'old lady' as she falls on her way out of Vanity Fair Oscars party USA baseball stars slammed over'disgraceful' national anthem gesture before WBC final vs Venezuela Israel says Iran's intelligence chief has been killed in overnight airstrike in latest attack on regime: Live updates Presidential hopeful JB Pritzker's bold defiant bet against black caucus pays off Supreme Court's top judge issues chilling warning as Trump targets his own appointees Heath Ledger's lookalike daughter Matilda steps out days after 17 year anniversary of late actor's Oscar win Fox News anchor issues blistering takedown of liberal media's delusional take on Iran: 'A stalemate? I ditched my realtor and used ChatGPT to sell my Florida house instead. Here's my exact prompts and steps for you to do it too Hollywood's top insider makes VERY catty observation about Kaitlan Collins Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with Mamdani forces New York beloved preschool to hike annual fee to $36,000... and parents are fuming Alix Earle stuns in white bikini in first glimpse at 2026 Sports Illustrated Swimsuit edition... after turning heads with Tom Brady and Joe Burrow Scientists reveal what a '30% chance of rain' REALLY means Are you always getting caught in the rain without an umbrella? If so, you might be reading your weather forecast app wrong. When many people see a '30% chance of rain' on their app, they think this corresponds to the heaviness of the downpour, or the area of land that will experience it.

Charles Bennett and Gilles Brassard pioneered quantum information theory. Now they've been awarded the highest honor in computer science. Today it's widely acknowledged that the future of computing will involve the quantum realm . Companies like Google, Microsoft, IBM, and a few well-funded startups are frantically building quantum computers and routinely claiming advances that seem to bring this exotic, world-changing technology within reach. In 1979 all of this was unthinkable.

Higgs Boson breakthrough was UK triumph, but British physics faces'catastrophic' cuts When the Nobel Prize in Physics was announced in Stockholm in October 2013, the world was watching. Among the names read out was Prof Peter Higgs, the British theorist who, nearly half a century earlier, had predicted the existence of a particle believed to hold the cosmos together - the Higgs boson. The announcement, broadcast live from Sweden, was what many scientists had hoped for since a year earlier, when experiments at CERN had finally confirmed Higgs's theory by discovering the Higgs boson - hailed as one of the biggest discoveries in a generation. At the time Higgs, who has since passed away, said in a statement: I hope this recognition of fundamental science will help raise awareness of the value of blue-sky research. Blue-sky research asks questions to understand the universe, rather than design new products.

Ugly new Nicole Kidman and Keith Urban divorce fight ERUPTS: Her friends share humiliating details of'midlife crisis'... and reveal brutal REAL reason daughter Sunday Rose'snubbed' him Supreme Court's top judge issues chilling warning as Trump targets his own appointees SARAH VINE: How telling that Meghan's joined the ranks of those peddling wellness and fake lifestyles to the gullible I moved my family OFF-GRID after a horrific series of events... now our tiny home saves us thousands each MONTH. We are richer and happier than ever. Here's how you can do it too Furious US troops erupt at CNN's $20m steak and lobster claims as grim photos expose reality Mother of cheating nurse shares horrific way daughter was killed after SUV sex... and shares heartbreaking details of her marriage to doctor Hollywood's top insider makes VERY catty observation about Kaitlan Collins CIA accused of'poisoning the sky' with toxins as files expose secret weather control agenda Mysterious'three-sided pyramid' similar to those in Egypt spotted on Mars in NASA footage Trump says he's'not afraid' of Vietnam-style ground combat in Iran I've always been embarrassed by my spotty skin. I'd tried every lotion and potion, until I found a science-backed plan that restored my skin's health and my confidence Alix Earle stuns in white bikini in first glimpse at 2026 Sports Illustrated Swimsuit edition... after turning heads with Tom Brady and Joe Burrow'We no longer need NATO': Trump sends shockwaves through Europe with ferocious attack on allies Everything JFK Jr told friends about his love affair with'sexual dynamo' Madonna... her unprintable pillow talk... and his perverse incest request that she couldn't go through with What your WALK says about you: Study reveals how your swagger can reveal how you're really feeling READ MORE: 'Tough guy' walk in western movies makes you look powerful A new study has revealed exactly what your walk says about you - whether it's a slow swagger or a peppy stride. Scientists from the Advanced Telecommunications Research Institute International in Japan carried out several experiments as part of their study.

Quantum Graphical Models (QGMs) generalize classical graphical models by adopting the formalism for reasoning about uncertainty from quantum mechanics. Unlike classical graphical models, QGMs represent uncertainty with density matrices in complex Hilbert spaces. Hilbert space embeddings (HSEs) also generalize Bayesian inference in Hilbert spaces. We investigate the link between QGMs and HSEs and show that the sum rule and Bayes rule for QGMs are equivalent to the kernel sum rule in HSEs and a special case of Nadaraya-Watson kernel regression, respectively. We show that these operations can be kernelized, and use these insights to propose a Hilbert Space Embedding of Hidden Quantum Markov Models (HSE-HQMM) to model dynamics. We present experimental results showing that HSE-HQMMs are competitive with state-of-the-art models like LSTMs and PSRNNs on several datasets, while also providing a nonparametric method for maintaining a probability distribution over continuous-valued features.

As datasets grow richer, an important challenge is to leverage the full features in the data to maximize the number of useful discoveries while controlling for false positives. We address this problem in the context of multiple hypotheses testing, where for each hypothesis, we observe a p-value along with a set of features specific to that hypothesis. For example, in genetic association studies, each hypothesis tests the correlation between a variant and the trait. We have a rich set of features for each variant (e.g. its location, conservation, epigenetics etc.) which could inform how likely the variant is to have a true association. However popular testing approaches, such as Benjamini-Hochberg's procedure (BH) and independent hypothesis weighting (IHW), either ignore these features or assume that the features are categorical. We propose a new algorithm, NeuralFDR, which automatically learns a discovery threshold as a function of all the hypothesis features. We parametrize the discovery threshold as a neural network, which enables flexible handling of multi-dimensional discrete and continuous features as well as efficient end-to-end optimization. We prove that NeuralFDR has strong false discovery rate (FDR) guarantees, and show that it makes substantially more discoveries in synthetic and real datasets. Moreover, we demonstrate that the learned discovery threshold is directly interpretable.