Vance grounded at White House as Iran peace talks in turmoil and Trump declares: 'I expect to be bombing' 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 Ritzy Bay Area town torn apart after teacher's daughter, 16, crashed car while speeding and killed four friends... then posted a TikTok video that poured fuel on the flames Jordon Hudson extends her control over Bill Belichick's empire with secret move that is set to leave his family and friends furious 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... Trump confronts Xi as US forces seize Chinese ship carrying mysterious'gift' to Iran Sydney Sweeney's role is cut from The Devil Wears Prada 2 Humiliating moment runner celebrates winning marathon... only to be pipped at the line by rival in brutal finish Patriots coach Mike Vrabel reveals'difficult conversations' with his wife as he speaks out for the first time since Dianna Russini photo scandal Nancy Mace fires back after accused sexual extorter Cory Mills tries to expel her from Congress: 'Bring it on' 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 Grieving mother says she went to LA school every day to complain daughter was being bullied... then tragedy struck when the lead tormentor, 12, hurled metal water bottle at victim's head Autistic woman, 24, worked hard to build independent life for herself... now she's PARALYZED thanks to selfishness of stranger READ MORE: Conjoined twin'influencers' are revealed to be AI AI influencers are cashing in on Coachella, with some set to make tens of thousands from their content. Among the celebrities and content creators, you may have noticed a surge in festival content from digital influencers.

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' 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' 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 Life-threatening cantaloupe recall in four states upgraded to FDA's highest risk level... 'reasonable probability of death' Fury as murderer marries pen pal behind bars... as teenage victim's mom says: 'I'm serving a life sentence without my son' Kate and William join Charles and Camilla in celebrating British centenarians at Buckingham Palace as Royal Family marks the late Queen's 100th birthday US troops board second tanker as Trump accuses Iran of violating ceasefire'numerous times' - Live updates 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 How to lose weight when perimenopause sabotages your metabolism: I'm a trainer but when I hit 46, I piled on the pounds overnight. I was losing hair so fast a bald spot the size of an orange appeared. I owe my life to a $1 at-home treatment that REVERSED the damage in a month.

Density ratio estimation (DRE) is a useful tool for quantifying discrepancies between probability distributions, but existing approaches often involve a trade-off between estimation quality and computational efficiency. Classical direct DRE methods are usually efficient at inference time, yet their performance can seriously deteriorate when the discrepancy between distributions is large. In contrast, score-based DRE methods often yield more accurate estimates in such settings, but they typically require considerable repeated function evaluations and numerical integration. We propose One-step Score-based Density Ratio Estimation (OS-DRE), a partly analytic and solver-free framework designed to combine these complementary advantages. OS-DRE decomposes the time score into spatial and temporal components, representing the latter with an analytic radial basis function (RBF) frame. This formulation converts the otherwise intractable temporal integral into a closed-form weighted sum, thereby removing the need for numerical solvers and enabling DRE with only one function evaluation. We further analyze approximation conditions for the analytic frame, and establish approximation error bounds for both finitely and infinitely smooth temporal kernels, grounding the framework in existing approximation theory. Experiments across density estimation, continual Kullback-Leibler and mutual information estimation, and near out-of-distribution detection demonstrate that OS-DRE offers a favorable balance between estimation quality and inference efficiency.

High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped in local modes when confronted with rugged or disconnected energy landscapes. This limits their ability to achieve adequate mixing and convergence in high-dimensional multimodal discrete spaces. To address these challenges, we propose \emph{Hyperbolic Secant-squared Gibbs-Sampling (HiSS)}, a novel family of sampling algorithms that integrates a \emph{Metropolis-within-Gibbs} framework to enhance mixing efficiency. HiSS leverages a logistic convolution kernel to couple the discrete sampling variable with the continuous auxiliary variable in a joint distribution. This design allows the auxiliary variable to encapsulate the true target distribution while facilitating easy transitions between distant and disconnected modes. We provide theoretical guarantees of convergence and demonstrate empirically that HiSS outperforms many popular alternatives on a wide variety of tasks, including Ising models, binary neural networks, and combinatorial optimization.

We develop parameter-free algorithms for unconstrained online learning with regret guarantees that scale with the gradient variation $V_T(u) = \sum_{t=2}^T \|\nabla f_t(u)-\nabla f_{t-1}(u)\|^2$. For $L$-smooth convex loss, we provide fully-adaptive algorithms achieving regret of order $\widetilde{O}(\|u\|\sqrt{V_T(u)} + L\|u\|^2+G^4)$ without requiring prior knowledge of comparator norm $\|u\|$, Lipschitz constant $G$, or smoothness $L$. The update in each round can be computed efficiently via a closed-form expression. Our results extend to dynamic regret and find immediate implications to the stochastically-extended adversarial (SEA) model, which significantly improves upon the previous best-known result [Wang et al., 2025].

As generative models enable rapid creation of high-fidelity images, societal concerns about misinformation and authenticity have intensified. A promising remedy is multi-bit image watermarking, which embeds a multi-bit message into an image so that a verifier can later detect whether the image is generated by someone and further identify the source by decoding the embedded message. Existing approaches often fall short in capacity, resilience to common image distortions, and theoretical justification. To address these limitations, we propose ADD (Add, Dot, Decode), a multi-bit image watermarking method with two stages: learning a watermark to be linearly combined with the multi-bit message and added to the image, and decoding through inner products between the watermarked image and the learned watermark. On the standard MS-COCO benchmark, we demonstrate that for the challenging task of 48-bit watermarking, ADD achieves 100\% decoding accuracy, with performance dropping by at most 2\% under a wide range of image distortions, substantially smaller than the 14\% average drop of state-of-the-art methods. In addition, ADD achieves substantial computational gains, with 2-fold faster embedding and 7.4-fold faster decoding than the fastest existing method. We further provide a theoretical analysis explaining why the learned watermark and the corresponding decoding rule are effective.

Data leakage remains a recurrent source of optimistic bias in biomedical machine learning studies. Standard row-wise cross-validation and globally estimated preprocessing steps are often inappropriate for data with repeated measurements, study-level heterogeneity, batch effects, or temporal dependencies. This paper describes bioLeak, an R package for constructing leakage-aware resampling workflows and for auditing fitted models for common leakage mechanisms. The package provides leakage-aware split construction, train-fold-only preprocessing, cross-validated model fitting, nested hyperparameter tuning, post hoc leakage audits, and HTML reporting. The implementation supports binary classification, multiclass classification, regression, and survival analysis, with task-specific metrics and S4 containers for splits, fits, audits, and inflation summaries. The simulation artifacts show how apparent performance changes under controlled leakage mechanisms, and the case study illustrates how guarded and leaky pipelines can yield materially different conclusions on multi-study transcriptomic data. The emphasis throughout is on software design, reproducible workflows, and interpretation of diagnostic output.

Deep learning underpins a wide range of applications in MRI, including reconstruction, artifact removal, and segmentation. However, progress has been driven largely by public datasets focused on brain and knee imaging, shaping how models are trained and evaluated. As a result, careful studies of the reliability of these models across diverse anatomical settings remain limited. In this work, we introduce MosaicMRI, a large and diverse collection of fully sampled raw musculoskeletal (MSK) MR measurements designed for training and evaluating machine-learning-based methods. MosaicMRI is the largest open-source raw MSK MRI dataset to date, comprising 2,671 volumes and 80,156 slices. The dataset offers substantial diversity in volume orientation (e.g., axial, sagittal), imaging contrasts (e.g., PD, T1, T2), anatomies (e.g., spine, knee, hip, ankle, and others), and numbers of acquisition coils. Using VarNet as a baseline for accelerated reconstruction task, we perform a comprehensive set of experiments to study scaling behavior with respect to both model capacity and dataset size. Interestingly, models trained on the combined anatomies significantly outperform anatomy-specific models in low-sample regimes, highlighting the benefits of anatomical diversity and the presence of exploitable cross-anatomical correlations. We further evaluate robustness and cross-anatomy generalization by training models on one anatomy (e.g., spine) and testing them on another (e.g., knee). Notably, we identify groups of body parts (e.g., foot and elbow) that generalize well with each other, and highlight that performance under domain shifts depends on both training set size, anatomy, and protocol-specific factors.

Estimating heterogeneous treatment effects in survival settings is complicated by right censoring as well as the time-varying nature of the estimand. While the conditional average treatment effect (CATE) provides a natural target, most existing approaches focus on a single prespecified time point and do not account for the temporal trajectory, leading to instability in estimation. We propose a deep survival learner (DSL) for estimating heterogeneous treatment effects with right-censored outcomes. The method is based on a doubly robust pseudo-outcome whose conditional expectation identifies time-specific CATEs under standard assumptions. This construction remains unbiased if either the outcome model or the treatment assignment model is correctly specified, when properly accounting for censoring. To estimate CATEs over a clinically relevant time spectrum, DSL employs a multi-output deep neural network with shared representations, enabling joint estimation of treatment effect trajectories. From a theoretical perspective, we derive error bounds for both pointwise and joint estimation over time. We show that joint estimation can leverage temporal structure to control estimation error without incurring much additional approximation cost under smoothness conditions, leading to improved stability relative to separate estimation. Cross-fitting is incorporated to reduce overfitting and mitigate bias arising from flexible nuisance estimation. Simulation studies demonstrate favorable finite-sample performance, particularly under nuisance model misspecification. Applied to the Boston Lung Cancer Study, DSL reveals heterogeneity in the effects of perioperative chemotherapy across patient characteristics and over time.

We consider the problem of clustering nested or hierarchical data, where observations are grouped and there are both group-level and observation-level variables. In our motivating OneK1K dataset, observations consist of single-cell RNA-sequencing (scRNA-seq) data from 982 individuals (groups), totaling 1.27 million cells (observations), along with individual-specific genotype data. This type of data would enable the identification of cell types and the investigation of how genetic variations among individuals influence differences in cell-type profiles. Our goal, therefore, is to jointly cluster cells and individuals to capture the heterogeneity across both levels using cell-specific gene expressions as well as individual-specific genotypes. However, existing grouped clustering methods do not incorporate group-level variables, thereby limiting their ability to capture the heterogeneity of genotypes in our motivating application. To address this, we propose the Nested Atoms Model (NAM), a new Bayesian nonparametric approach that enables the desired two-layered clustering, accounting for both group-level and observation-level variables. To scale NAM for high-dimensional data, we develop a fast variational Bayesian inference algorithm. Simulations show that NAM outperforms existing methods that ignore group-level variables. Applied to the OneK1K dataset, NAM identifies clusters of genetically similar individuals with homogeneous cell-type profiles. The resulting cell clusters align with known immune cell types based on differential gene expression, underscoring the ability of NAM to capture nested heterogeneity and provide biologically meaningful insights.