Epstein's ultimate betrayal of Trump as emails reveal billionaire's twisted plot against president: 'I am the one able to take him down' Father of cheerleader who mysteriously died on Carnival cruise speaks out on investigation... and reveals the horrific theories he's heard I tried the'magic' pill that claims to cure migraines, back pain, anxiety and insomnia. The relief was instant... and it costs just $25 a month The REAL reason why Prince Harry and Meghan Markle photos were removed from Kris Jenner's birthday posts Kim Kardashian's daughter North West, 12, shocks fans with'high-risk piercing' not suitable for kids Alex Murdaugh's housekeeper says she KNEW the lawyer killed his wife and son in bombshell new book Civil rights leader Rev. Jesse Jackson hospitalized in Chicago Donald Trump leaves Ozzy Osbourne's widow Sharon in tears after paying tribute to the late rocker Kelly Clarkson's staff'feel like s***': TV insiders reveal star's huge backstage transformation after death of ex-husband He killed his daughter, 2, in a hot car then committed suicide on day he was due to be jailed. Then she tried to have her rich husband assassinated. Epstein's mysterious falling out with Clinton is revealed in emails to Obama lawyer inviting her to his infamous NYC townhouse John Travolta's son Benjamin, 14, has grown into his spitting image as Grease star proudly shares new clip Sober Dolphins coach Mike McDaniel'indebted' to Commanders' Dan Quinn for helping him beat drinking problem Diddy has prison release date pushed BACK amid allegations of'drinking moonshine' Three winters into Putin's savage war, his battered army is devouring itself. Trump makes sordid joke about Muslim president's WIFE at the White House The Navy commander who stared down Al Qaeda on the USS Cole has a new enemy... and a chilling warning for America Scientists have cracked the code behind a mysterious language discovered among a non-human species living in Earth's oceans that mirrors human speech.

Since September, residents on South Korea's Jeju island have been spotting small packs of what appear to be bags of Chinese tea washed ashore. Upon closer inspection, however, they were found to contain ketamine. Some 28kg (62 lbs) of the drug, wrapped in foil and labelled with the Chinese character for tea, have been found on at least eight occasions, police say. Ketamine is used as an anaesthetic in medical procedures, but its recreational use is illegal in South Korea. It can cause severe physical and mental damage, including to the heart and lungs, when misused.

China's AI is quietly making big inroads in Silicon Valley China's AI models are quickly gaining traction in Silicon Valley, becoming integral to the operations of American companies and earning the praise of a growing list of tech leaders. Their rapid ascent has highlighted the competitive edge that Chinese developers such as Alibaba, Z.ai, Moonshot, and MiniMax have been able to gain by offering so-called "open" language models at much lower costs than their rivals in the United States. Airbnb CEO Brian Chesky generated headlines in October when he revealed that the short-term rental platform had opted for Alibaba's Qwen over OpenAI's ChatGPT, praising the Chinese model as "fast and cheap". Social Capital CEO Chamath Palihapitiya revealed the same month that his company had migrated much of its work to Moonshot's Kimi K2 as it was "way more performant" and "a ton cheaper" than models from OpenAI and Anthropic. Programmers on social media also recently highlighted evidence that two popular US-developed coding assistants, Composer and Windsurf, were built on Chinese models.

Is the fall of Pokrovsk inevitable? Is Trump losing patience with Putin? Will sanctions against Russian oil giants hurt Putin? Russian forces launched 645 attacks on Ukraine's Zaporizhia region in the past day, killing one person in the Polohivskyi district, Governor Ivan Fedorov wrote in a post on Telegram. A Russian drone attack on a railway facility killed a security guard in Ukraine's Kherson region, Governor Oleksandr Prokudin wrote in a post on Facebook.

Mamdani ran against New York City's political establishment. Do his early appointments suggest he's preparing to work within it? The staff writer Eric Lach joins Tyler Foggatt to discuss Zohran Mamdani's victory in the New York City mayoral race, and what his time in office might look like. They talk about some of his early appointments to his administration and how his ambitious agenda may be at odds with other wings of the Democratic Party. They also look at how members of both parties are interpreting Mamdani's win, and how the new mayor might respond to President Donald Trump's threats to withhold federal funds from the city.

Reward machines (RMs) are automata structures that encode (non-Markovian) reward functions for reinforcement learning (RL). RMs can reward any behaviour representable in regular languages and, when paired with RL algorithms that exploit RM structure, have been shown to significantly improve sample efficiency in many domains. In this work, we present pushdown reward machines (pdRMs), an extension of reward machines based on deterministic pushdown automata. pdRMs can recognise and reward temporally extended behaviours representable in deterministic context-free languages, making them more expressive than reward machines. We introduce two variants of pdRM-based policies, one which has access to the entire stack of the pdRM, and one which can only access the top $k$ symbols (for a given constant $k$) of the stack. We propose a procedure to check when the two kinds of policies (for a given environment, pdRM, and constant $k$) achieve the same optimal state values. We then provide theoretical results establishing the expressive power of pdRMs, and space complexity results for the proposed learning problems. Lastly, we propose an approach for off-policy RL algorithms that exploits counterfactual experiences with pdRMs. We conclude by providing experimental results showing how agents can be trained to perform tasks representable in deterministic context-free languages using pdRMs.

Recent work on latent diffusion models (LDMs) has focused almost exclusively on generative tasks, leaving their potential for discriminative transfer largely unexplored. We introduce Discriminative Vicinity Diffusion (DVD), a novel LDM-based framework for a more practical variant of source-free domain adaptation (SFDA): the source provider may share not only a pre-trained classifier but also an auxiliary latent diffusion module, trained once on the source data and never exposing raw source samples. DVD encodes each source feature's label information into its latent vicinity by fitting a Gaussian prior over its k-nearest neighbors and training the diffusion network to drift noisy samples back to label-consistent representations. During adaptation, we sample from each target feature's latent vicinity, apply the frozen diffusion module to generate source-like cues, and use a simple InfoNCE loss to align the target encoder to these cues, explicitly transferring decision boundaries without source access. Across standard SFDA benchmarks, DVD outperforms state-of-the-art methods. We further show that the same latent diffusion module enhances the source classifier's accuracy on in-domain data and boosts performance in supervised classification and domain generalization experiments. DVD thus reinterprets LDMs as practical, privacy-preserving bridges for explicit knowledge transfer, addressing a core challenge in source-free domain adaptation that prior methods have yet to solve.

The Kalman filter and Rauch-Tung-Striebel (RTS) smoother are optimal for state estimation in linear dynamic systems. With nonlinear systems, the challenge consists in how to propagate uncertainty through the state transitions and output function. For the case of a neural network model, we enable accurate uncertainty propagation using a recent state-of-the-art analytic formula for computing the mean and covariance of a deep neural network with Gaussian input. We argue that cross entropy is a more appropriate performance metric than RMSE for evaluating the accuracy of filters and smoothers. We demonstrate the superiority of our method for state estimation on a stochastic Lorenz system and a Wiener system, and find that our method enables more optimal linear quadratic regulation when the state estimate is used for feedback.