You're viewing the US edition You can switch to the UK or AU homepage at any time using this menu. Trump's CIA chief John Ratcliffe makes surprise trip to Moscow for secret meeting amid grim fears for Poland Hoover Dam's horror threat to 40 million Americans: As'tipping point' is reached... expert warns residents in THREE states to brace There's only one way Harry and Meghan's new royal life in Britain can work... and she's going to hate it: ROBERT JOBSON The photos that sparked wild internet rumours: James Blunt mingles with Hayden Panettiere on a yacht in 2009 after he broke his silence on claims he was the'British singer' who the late actress was put into bed with aged 18 Lindsay Clancy's lawyer clashes with witness as tensions reach fever pitch after exploding at reporter outside: Live updates Vanity Fair journalist covering Lindsay Clancy trial sparks outrage for SMILING on camera as she says'I'm proud of myself' in face of backlash ALEXANDRA SHULMAN: Emotionally battered, physically scarred... and I've put on weight. But I'm still in my bikini at 68, and this is why you should follow my lead Hollywood's nepo babies take over Vanity Fair's best dressed list: North West, Beyoncé's eldest Blue Ivy and Meryl Streep's daughter land top spots Your next new car could cost up to $6,000 more if President Trump's 50% tariff on Canada goes into effect Brand-new penis enlargement technique increased this man's size by a THIRD in just 45 minutes... he bares all and reveals results that've left him thrilled The 10-cent supplement that turbocharges your Mounjaro AND reduces your cholesterol: Most patients won't have heard of it, but now experts reveal why anyone on jabs must take it - and how it can stop you putting weight back on Renters rejoice as feds put an end to Zillow's $100M plot to neuter rival Redfin and eliminate rental market competition Brian Hickerson's dark family secrets outed by his own sister... who reveals moment his'demons' took over... and real reason Hayden Panettiere kept going back Woke Boston mayor goes on fever-pitched hunt to track down and threaten business owners renting parking spots to ICE agents in her city: 'This is unhinged' Lawyers for Anna Kepner's stepbrother make desperate bid to delay murder trial as they grapple with'unique and very unfortunate' evidence into Carnival cruise death Prince Harry and Meghan are'not the same people who left' and'relate to Britain differently', says Omid Scobie I left a sexless marriage at 54. Now, I'm having the time of my life with men in their 20s and 30s. This is what they all love about me...and why I'll still keep having our sleepovers in hotel rooms The Bible describes Jesus' burial place as a tomb carved into rock, set inside a garden near where he was crucified. For nearly 1,700 years, Christians have believed that tomb lies within Jerusalem's Church of the Holy Sepulchre.

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The US and Israel have signed a deal allocating land for a permanent US embassy in West Jerusalem, years after a temporary one was established during Trump's first term in office. The move is yet another blow to the hopes of a future Palestinian capital. How AI is being weaponised against India's Muslim women

'This is an apartheid regime' Far-right Israeli minister Itamar Ben Gvir stormed the Al-Aqsa compound under heavy military protection during Jerusalem Day, as Israelis marched through occupied East Jerusalem. The march marks Israel's 1967 capture and illegal occupation of East Jerusalem. Iran's FM urges BRICS states to condemn US-Israeli aggression

Ritzy Bay Area town torn apart after teacher's daughter, 16, was behind wheel when four friends died in high-speed crash... then she posted a TikTok video that poured fuel on the flames Two CIA officers killed in Mexico when their car skidded off ravine and exploded after meeting about bust of'largest ever drug lab' Nancy Guthrie sheriff's appalling past revealed: Beat handcuffed suspect so badly he needed intensive care, used VILE language about woman and lied in sworn statement Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran New'Hollywood dose' pill: A-listers hooked on'youth elixir' that dermatologists say is anti-ageing, shrinks pores, smooths wrinkles... and even banishes rosacea Days after we got engaged, the love of my life told me he'd killed a man and buried him in a bog. I reported him to police... but then I made this irreversible mistake Ark of the Covenant's final resting place pinpointed by archaeologists as fresh search begins Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Insiders claim failed AI rollout could be to blame for Tim Cook's departure from Apple - as one says'the AI era requires a different kind of leadership' Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' AMANDA PLATELL: Why Sarah Ferguson - with the ghost of Princess Diana at her side - is ready to sensationally blow up the Royal Family. She knows ALL their secrets... Team USA Olympics star Noah Lyles slammed for'horrible' reaction to his wife's wedding dress reveal In honour of the Queen's (purple!) reign: Kate mirrors late monarch's colourful wardrobe and wears her pearl earrings and necklace US troops board second tanker as Iran is accused of breaking ceasefire'numerous times' How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. The new'posh' drug that's easier to order than Uber Eats - and why all my middle-class friends have ditched booze and cocaine for it: JANA HOCKING Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger The video game where you play as JESUS: Open-world simulator lets you'follow the path' of the Messiah as he is baptized, perform miracles, fights the Devil and gets CRUCIFIED READ MORE: Rare marble artefact discovered in the'cradle of Christianity' While fans eagerly await the release of Grand Theft Auto 6, one Polish game studio has unveiled a rather unorthodox alternative. The video game, titled'I Am Jesus Christ' allows players to'walk in the footsteps of Jesus' in an immersive first-person retelling of the gospel.

What are the limits of controlling language models via synthetic training data? We develop a reinforcement learning (RL) primitive, the Dataset Policy Gradient (DPG), which can precisely optimize synthetic data generators to produce a dataset of targeted examples. When used for supervised fine-tuning (SFT) of a target model, these examples cause the target model to do well on a differentiable metric of our choice. Our approach achieves this by taking exact data attribution via higher-order gradients and using those scores as policy gradient rewards. We prove that this procedure closely approximates the true, intractable gradient for the synthetic data generator. To illustrate the potential of DPG, we show that, using only SFT on generated examples, we can cause the target model's LM head weights to (1) embed a QR code, (2) embed the pattern $\texttt{67}$, and (3) have lower $\ell^2$ norm. We additionally show that we can cause the generator to (4) rephrase inputs in a new language and (5) produce a specific UUID, even though neither of these objectives is conveyed in the generator's input prompts. These findings suggest that DPG is a powerful and flexible technique for shaping model properties using only synthetic training examples.

Motifs often recur in musical works in altered forms, preserving aspects of their identity while undergoing local variation. This paper investigates how such motivic transformations occur within their musical context in symbolic music. To support this analysis, we develop a probabilistic framework for modeling motivic transformations and apply it to Beethoven's piano sonatas by integrating multiple datasets that provide melodic, rhythmic, harmonic, and motivic information within a unified analytical representation. Motif transformations are represented as multilabel variables by comparing each motif instance to a designated reference occurrence within its local context, ensuring consistent labeling across transformation families. We introduce a multilabel Conditional Random Field to model how motif-level musical features influence the occurrence of transformations and how different transformation families tend to co-occur. Our goal is to provide an interpretable, distributional analysis of motivic transformation patterns, enabling the study of their structural relationships and stylistic variation. By linking computational modeling with music-theoretical interpretation, the proposed framework supports quantitative investigation of musical structure and complexity in symbolic corpora and may facilitate the analysis of broader compositional patterns and writing practices.

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics. This paper introduces a framework for jointly learning the state, dynamics, and parameters of filtering algorithms in data assimilation through a process we refer to as auto-differentiable filtering. The framework leverages a theoretically motivated loss function that enables learning from partial, noisy observations via gradient-based optimization using auto-differentiation. We further demonstrate how several well-known data assimilation methods can be learned or tuned within this framework. To underscore the versatility of auto-differentiable filtering, we perform experiments on dynamical systems spanning multiple scientific domains, such as the Clohessy-Wiltshire equations from aerospace engineering, the Lorenz-96 system from atmospheric science, and the generalized Lotka-Volterra equations from systems biology. Finally, we provide guidelines for practitioners to customize our framework according to their observation model, accuracy requirements, and computational budget.

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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 .