Poodle crossbreeds have grown overwhelmingly popular, sparking controversy in dog parks and kennel clubs alike. The features of doodles such as Peaches (above), a goldendoodle, have become the canine equivalent of Instagram face. Meet the Breeds, the American Kennel Club's annual showcase of purebred dogs, took place over two eye-wateringly cold days in early February at the Javits Center, in Manhattan. About a hundred and fifty of the two hundred and five varieties recognized as official breeds by the A.K.C., the long-standing authority in the U.S. dog world, were in attendance for the public to ogle, fondle, and coo "So cute!" to, including the basset fauve de Bretagne, a hunting hound from France that's one of three newly recognized breeds recently allowed into the purebred pantheon. Some of the dogs had competed in the Westminster Kennel Club Dog Show earlier in the week, and past champions had their ribbons on display. In spite of the frigid weather, pavilions hosting the more popular breeds--the pug, the Doberman pinscher, the Great Dane, the St. Bernard--were packed. Lesser-known varieties, such as the saluki, the Löwchen, and the Lapponian herder, drew sparser crowds. There were exhibition spaces for each breed, and on the back walls were three adjectives supposedly describing that particular type of dog's temperament. There is, in fact, no evidence that temperament is consistent within a breed, but the idea is deeply rooted in dogdom. I stopped to caress the velvety ear leather of a pharaoh hound ("Friendly, Smart, Noble"), a sprinting breed once used to hunt rabbits in Malta; accept kisses from a Portuguese water dog, bred to assist with retrieving tackle ("Affectionate, Adventurous, Athletic"); and have my photograph taken with a Leonberger, a German breed from the town of Leonberg, in southwest Germany ("Friendly, Gentle, Playful"). No one was supposed to be openly selling dogs, but, if you asked, the breeders would share their information. Excluding what are known as companion dogs, like the Leonberger, most of the animals at the show were designed for a purpose that is no longer required of them. In Great Britain, foxhounds are legally barred from chasing foxes. Consider the fate of the otterhound, an ancient variety with a noble heritage which was once used in the U.K. to hunt river otters, which were prized for their thick fur and disliked by wealthy landowners because they ate fish in their stocked ponds.

Tue 16 Dec 2025 08.00 ESTLast modified on Tue 16 Dec 2025 08.02 EST The sign outside Tom Hermes's farmyard in Perkins Township in Ohio, a short drive south of the shores of Lake Erie, proudly claims that his family have farmed the land here since 1900. Today, he raises 130 head of cattle and grows corn, wheat, grass and soybeans on 1,200 acres of land. For his family, his animals and wider business, water is life. So when, in May 2024, the Texas-based Aligned Data Centers broke ground on its NEO-01, four-building, 200,000 sq ft data center on a brownfield site that abuts farmland that Hermes rents, he was concerned. "We have city water here. That's going to reduce the pressure if they are sucking all the water," he says of the data center.

This work investigates the structural properties, cycloid trajectories, and non-asymptotic convergence guarantees of the Expectation-Maximization (EM) algorithm for two-component Mixed Linear Regression (2MLR) with unknown mixing weights and regression parameters. Recent studies have established global convergence for 2MLR with known balanced weights and super-linear convergence in noiseless and high signal-to-noise ratio (SNR) regimes. However, the theoretical behavior of EM in the fully unknown setting remains unclear, with its trajectory and convergence order not yet fully characterized. We derive explicit EM update expressions for 2MLR with unknown mixing weights and regression parameters across all SNR regimes and analyze their structural properties and cycloid trajectories. In the noiseless case, we prove that the trajectory of the regression parameters in EM iterations traces a cycloid by establishing a recurrence relation for the sub-optimality angle, while in high SNR regimes we quantify its discrepancy from the cycloid trajectory. The trajectory-based analysis reveals the order of convergence: linear when the EM estimate is nearly orthogonal to the ground truth, and quadratic when the angle between the estimate and ground truth is small at the population level. Our analysis establishes non-asymptotic guarantees by sharpening bounds on statistical errors between finite-sample and population EM updates, relating EM's statistical accuracy to the sub-optimality angle, and proving convergence with arbitrary initialization at the finite-sample level. This work provides a novel trajectory-based framework for analyzing EM in Mixed Linear Regression.

'Arc de Trump' designed by president unveiled as he reveals controversial past plan for monument site'Vile' American flag spotted in Republican's office sparks Capitol investigation Experts reveal five-day window when'life-threatening' storm is set to smash US as it brews in Atlantic Ocean RICHARD EDEN: The VERY telling video that suggests one of Meghan's closest confidants has been'Markled'. He once leapt to her defence... now like so many others he needs to watch his step She's the dancer caught'going at it' in bed with Britney Spears. Nepo babies dare to bare! Celebrity offspring leave nothing to imagination as they dominate Victoria's Secret show... what would their parents say? Nightmarish moment train door closes on 65-year-old man's coat and drags him to his death MAUREEN CALLAHAN: Trump's depraved critics have committed their foulest act yet... Bella Hadid's health battle takes dark turn: Loved ones reveal hellish new details about model... as ominous texts emerge Why'embarrassed' Keith Urban is'in hiding' amid divorce from wife Nicole Kidman Disney superfan, 31, vanishes from her Midwest home months after announcing pregnancy... then horrific discovery is made at Walt Disney World Selena Gomez admits she was'sobbing' and fearing the worst just WEEKS after marrying music producer Benny Blanco in lavish ceremony Race against time to build a 211-mile gravel track across America's most extreme frontier for new'Manhattan Project'... but it could be too late Victoria's Secret show 2025: Bella Hadid rules the runway after her health woes, Jasmine Tookes opens the show at nine months pregnant and Emily Ratajkowski makes her debut aged 34 as legendary Angels and nepo babies unite after failed woke rebrand Red-eyed female executive, 61, with $1.1m home attacked two Alaska Airlines staff and forced plane to make emergency landing, police say Most shocking moments from female-fronted talk show dubbed'The View for conservatives' Nancy Pelosi explodes at reporter as she's escorted down Capitol Building steps Is this why aliens haven't contacted us yet? READ MORE: Reaching out to aliens could result in'the end of all life on Earth' It's one of the biggest unanswered questions in science: if there's life beyond Earth, why hasn't it contacted us yet?

'Arc de Trump' designed by president unveiled as he reveals controversial past plan for monument site'Vile' American flag spotted in Republican's office sparks Capitol investigation Experts reveal five-day window when'life-threatening' storm is set to smash US as it brews in Atlantic Ocean RICHARD EDEN: The VERY telling video that suggests one of Meghan's closest confidants has been'Markled'. He once leapt to her defence... now like so many others he needs to watch his step She's the dancer caught'going at it' in bed with Britney Spears. Nepo babies dare to bare! Celebrity offspring leave nothing to imagination as they dominate Victoria's Secret show... what would their parents say? Nightmarish moment train door closes on 65-year-old man's coat and drags him to his death MAUREEN CALLAHAN: Trump's depraved critics have committed their foulest act yet... Bella Hadid's health battle takes dark turn: Loved ones reveal hellish new details about model... as ominous texts emerge Why'embarrassed' Keith Urban is'in hiding' amid divorce from wife Nicole Kidman Disney superfan, 31, vanishes from her Midwest home months after announcing pregnancy... then horrific discovery is made at Walt Disney World Selena Gomez admits she was'sobbing' and fearing the worst just WEEKS after marrying music producer Benny Blanco in lavish ceremony Race against time to build a 211-mile gravel track across America's most extreme frontier for new'Manhattan Project'... but it could be too late Victoria's Secret show 2025: Bella Hadid rules the runway after her health woes, Jasmine Tookes opens the show at nine months pregnant and Emily Ratajkowski makes her debut aged 34 as legendary Angels and nepo babies unite after failed woke rebrand Red-eyed female executive, 61, with $1.1m home attacked two Alaska Airlines staff and forced plane to make emergency landing, police say Most shocking moments from female-fronted talk show dubbed'The View for conservatives' Nancy Pelosi explodes at reporter as she's escorted down Capitol Building steps Experts reveal five-day window when'life-threatening' storm is set to smash US as it brews in Atlantic Ocean A powerful tropical system brewing in the Atlantic Ocean could become the next major threat to lives and property in the US, meteorologists have warned. Forecasters are tracking a tropical wave, a poorly organized area of showers and thunderstorms, currently located off the coast of Africa, which is expected to develop into a named storm between October 21 and 25.

Nancy Pelosi explodes at reporter as she's escorted down Capitol Building steps Trump threatens'land strikes' on Venezuela as CIA begins covert operations in Latin American country and Maduro declares'No to coups' She's the dancer caught'going at it' in bed with Britney Spears. Bella Hadid's health battle takes dark turn: Loved ones reveal hellish new details about model... as ominous texts emerge Diane Keaton's cause of death revealed just days after actress' passing at 79 as her family pens emotional message to fans Emily Ratajkowski fans rejoice as she makes Victoria's Secret show debut at age 34 Murderer's final words and hearty last meal as he's executed after 30 years on death row Nepo babies dare to bare! Celebrity offspring leave nothing to imagination as they dominate Victoria's Secret show... what would their parents say? Victoria's Secret show 2025: Bella Hadid rules the runway after her health woes, Jasmine Tookes opens the show at nine months pregnant and Emily Ratajkowski makes her debut aged 34 as legendary Angels and nepo babies unite after failed woke rebrand Popular food can be used to fight resistant viruses ... and it costs just pennies Disney superfan, 31, vanishes from her Midwest home months after announcing pregnancy... then horrific discovery is made at Walt Disney World Chilling new footage shows knifeman on night he'stabbed Ukrainian refugee to death' on a train in murder that shook America Britney Spears unleashes on ex Kevin Federline AND her SONS - accusing him of'gaslighting' and claiming she's seen one boy for just 45 minutes in five years Jailed Diddy's harsh reality check as very unglamorous conditions rapper has to abide by after prison revealed Mel Gibson's highly-anticipated sequel to The Passion of the Christ has sparked outrage from fans, after it was revealed that it is moving forward with a new cast due to the time gap. The original 2004 movie followed the final 12 hours of Jesus Christ's life, and starred Jim Caviezel, 57, as Christ. However, The Resurrection of the Christ -- which takes place three days after Christ's crucifixion on Good Friday -- will now star Finnish actor Jaakko Ohtonen, 36, in the role of Christ.

Nancy Pelosi explodes at reporter as she's escorted down Capitol Building steps Trump threatens'land strikes' on Venezuela as CIA begins covert operations in Latin American country and Maduro declares'No to coups' She's the dancer caught'going at it' in bed with Britney Spears. Bella Hadid's health battle takes dark turn: Loved ones reveal hellish new details about model... as ominous texts emerge Diane Keaton's cause of death revealed just days after actress' passing at 79 as her family pens emotional message to fans Emily Ratajkowski fans rejoice as she makes Victoria's Secret show debut at age 34 Murderer's final words and hearty last meal as he's executed after 30 years on death row Nepo babies dare to bare! Celebrity offspring leave nothing to imagination as they dominate Victoria's Secret show... what would their parents say? Victoria's Secret show 2025: Bella Hadid rules the runway after her health woes, Jasmine Tookes opens the show at nine months pregnant and Emily Ratajkowski makes her debut aged 34 as legendary Angels and nepo babies unite after failed woke rebrand Popular food can be used to fight resistant viruses ... and it costs just pennies Disney superfan, 31, vanishes from her Midwest home months after announcing pregnancy... then horrific discovery is made at Walt Disney World Chilling new footage shows knifeman on night he'stabbed Ukrainian refugee to death' on a train in murder that shook America Meghan-linked charity is hit by racism and sexism allegations as staff claim it is a'toxic' and'hostile' workplace Britney Spears unleashes on ex Kevin Federline AND her SONS - accusing him of'gaslighting' and claiming she's seen one boy for just 45 minutes in five years Jailed Diddy's harsh reality check as very unglamorous conditions rapper has to abide by after prison revealed Scientists reveal the surprising age at which your brain reaches its peak - so, are YOUR best days behind you? READ MORE: Actor Tom Hanks thinks 35 is the hardest age - but is he right? With each passing day, you may feel like you're getting further past your peak.

Nancy Pelosi explodes at reporter as she's escorted down Capitol Building steps Trump threatens'land strikes' on Venezuela as CIA begins covert operations in Latin American country and Maduro declares'No to coups' She's the dancer caught'going at it' in bed with Britney Spears. Bella Hadid's health battle takes dark turn: Loved ones reveal hellish new details about model... as ominous texts emerge Diane Keaton's cause of death revealed just days after actress' passing at 79 as her family pens emotional message to fans Emily Ratajkowski fans rejoice as she makes Victoria's Secret show debut at age 34 Murderer's final words and hearty last meal as he's executed after 30 years on death row Nepo babies dare to bare! Celebrity offspring leave nothing to imagination as they dominate Victoria's Secret show... what would their parents say? Victoria's Secret show 2025: Bella Hadid rules the runway after her health woes, Jasmine Tookes opens the show at nine months pregnant and Emily Ratajkowski makes her debut aged 34 as legendary Angels and nepo babies unite after failed woke rebrand Popular food can be used to fight resistant viruses ... and it costs just pennies Disney superfan, 31, vanishes from her Midwest home months after announcing pregnancy... then horrific discovery is made at Walt Disney World Chilling new footage shows knifeman on night he'stabbed Ukrainian refugee to death' on a train in murder that shook America Britney Spears unleashes on ex Kevin Federline AND her SONS - accusing him of'gaslighting' and claiming she's seen one boy for just 45 minutes in five years Jailed Diddy's harsh reality check as very unglamorous conditions rapper has to abide by after prison revealed Britain has experienced its first official'MEGA FIRE' - and scientists warn the devastating blazes could soon become the norm READ MORE: Scientists warn that'FIREWAVES' will devastate UK cities Britain has experienced its first official'mega fire' - and scientists warn the devastating blazes could soon become the norm. Back in June, the Carrbridge and Dava Moor in the Scottish Highlands was devastated by the worst wildfire in living memory. The blaze burned over 11,000 hectares (42.5 square miles) of forest and peatland, killing thousands of animals in its path.

Agentic Retrieval-Augmented Generation (Agentic RAG) enhances the processing capability for complex tasks through dynamic retrieval and adaptive workflows. Recent advances (e.g., Search-R1) have shown that outcome-supervised reinforcement learning demonstrate strong performance. However, this approach still suffers from inefficient exploration, sparse reward signals, and ambiguous global reward feedback. To address these challenges, we propose DecEx-RAG, which models RAG as a Markov Decision Process (MDP) incorporating decision-making and execution, while introducing an efficient pruning strategy to optimize data expansion. Through comprehensive process-level policy optimization, DecEx-RAG significantly enhances the autonomous task decomposition, dynamic retrieval, and high-quality answer generation capabilities of large language models (LLMs). Experiments show that DecEx-RAG achieves an average absolute performance improvement of $6.2\%$ across six datasets, significantly outperforming existing baselines. Moreover, the pruning strategy improves data construction efficiency by nearly $6 \times$, providing an efficient solution for process-supervised RAG training. The code is available at https://github.com/sdsxdxl/DecEx-RAG.

Fine-scale soil mapping in Alaska, traditionally relying on fieldwork and localized simulations, remains a critical yet underdeveloped task, despite the region's ecological importance and extensive permafrost coverage. As permafrost thaw accelerates due to climate change, it threatens infrastructure stability and key ecosystem services, such as soil carbon storage. High-resolution soil maps are essential for characterizing permafrost distribution, identifying vulnerable areas, and informing adaptation strategies. We present MISO, a vision-based machine learning (ML) model to produce statewide fine-scale soil maps for near-surface permafrost and soil taxonomy. The model integrates a geospatial foundation model for visual feature extraction, implicit neural representations for continuous spatial prediction, and contrastive learning for multimodal alignment and geo-location awareness. We compare MISO with Random Forest (RF), a traditional ML model that has been widely used in soil mapping applications. Spatial cross-validation and regional analysis across Permafrost Zones and Major Land Resource Areas (MLRAs) show that MISO generalizes better to remote, unseen locations and achieves higher recall than RF, which is critical for monitoring permafrost thaw and related environmental processes. These findings demonstrate the potential of advanced ML approaches for fine-scale soil mapping and provide practical guidance for future soil sampling and infrastructure planning in permafrost-affected landscapes. The project will be released at https://github.com/knowledge-computing/Peatland-permafrost.