What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? Russian tanker struck off Turkiye as Ukraine targets'shadow fleet' A Russian-flagged tanker in the Black Sea has reported being attacked off the Turkish coast, the third such vessel to have been targeted within a week. The Turkish Directorate General of Maritime Affairs said on Tuesday that the Midvolga-2 had reported coming under attack about 130km (80 miles) from land.

UK share values'most stretched' since 2008, Bank warns The Bank of England has warned of a sharp correction in the value of major tech companies with growing fears of an artificial intelligence (AI) bubble. It said share prices in the UK are close to the most stretched they have been since the 2008 global financial crisis, while equity valuations in the US are reminiscent of those before the dotcom bubble burst. The central bank's financial stability report warned valuations are particularly stretched for companies focused on AI. It said the growth of the sector in the next five years would be fuelled by trillions of dollars of debt, raising financial stability risks if the value of the companies falls. The Bank of England cited industry figures forecasting spending on AI infrastructure could top $5tn (£3.8tn).

Italian luxury fashion house Valentino is facing criticism after posting disturbing adverts made using artificial intelligence (AI) for one of its luxury handbags online. The brand announced a collaboration with digital artists as part of what it dubbed a digital creative project promoting its new DeVain handbag. But an AI-generated advert it posted on Instagram has been met with intense criticism from fans, who called the visuals - and use of AI - sloppy and sad. The BBC has approached Valentino for comment. The Instagram post promoting the handbag, which has a label to say it was made using AI, shows a surreal collage of models spliced between Valentino logos and its DeVain bag.

What is in the 28-point US plan for Ukraine? 'Ukraine is running out of men, money and time' Can the US get all sides to end the war? Why is Europe opposing Trump's peace plan? Zelenskyy says US peace plan'looks better' with new revisions Here's where things stand on Tuesday, December 2: Russian forces launched a ballistic missile on Ukraine's Dnipro, killing four people and wounding 40 others, according to Ukrainian authorities. Russia claimed the capture of the strategic eastern Ukrainian town of Pokrovsk, the logistics hub that has been under attack for months by Moscow's forces.

The shock resignation came for a very specific reason, but the OBR saga will continue with a series of decisions the chancellor will have to make over Richard Hughes' replacement. Firstly the Chancellor will have to find a respected and credible economist to run the OBR. There are several candidates, who might fit the mould of fiercely independent bean counters. The list will be carefully watched by the markets for any departure from the normal model. The problem is that there is some political pressure to do just that.

The snakes behind the blockbuster are megafauna throwbacks. Breakthroughs, discoveries, and DIY tips sent every weekday. At roughly the length of a small school bus, anacondas are famously some of the world's largest snakes. Now fossil evidence proves that these enormous reptiles are also glimpses of an ancient world. According to a study published on December 1st in the, anacondas reached their maximum length around 12.4 million years ago--and have remained giants ever since.

Foundation models have become central to unifying perception and planning in robotics, yet real-world deployment exposes a mismatch between their monolithic assumption that a single model can handle all cognitive functions and the distributed, dynamic nature of practical service workflows. Vision-language models offer strong semantic understanding but lack embodiment-aware action capabilities while relying on hand-crafted skills. Vision-Language-Action policies enable reactive manipulation but remain brittle across embodiments, weak in geometric grounding, and devoid of proactive collaboration mechanisms. These limitations indicate that scaling a single model alone cannot deliver reliable autonomy for service robots operating in human-populated settings. To address this gap, we present InteractGen, an LLM-powered multi-agent framework that decomposes robot intelligence into specialized agents for continuous perception, dependency-aware planning, decision and verification, failure reflection, and dynamic human delegation, treating foundation models as regulated components within a closed-loop collective. Deployed on a heterogeneous robot team and evaluated in a three-month open-use study, InteractGen improves task success, adaptability, and human-robot collaboration, providing evidence that multi-agent orchestration offers a more feasible path toward socially grounded service autonomy than further scaling standalone models.

Bipartite networks are widely used to encode the ecological interactions. Being able to compare the organization of bipartite networks is a first step toward a better understanding of how environmental factors shape community structure and resilience. Yet current methods for structure detection in bipartite networks overlook shared patterns across collections of networks. We introduce the \emph{colBiSBM}, a family of probabilistic models for collections of bipartite networks that extends the classical Latent Block Model (LBM). The proposed framework assumes that networks are independent realizations of a shared mesoscale structure, encoded through common inter-block connectivity parameters. We establish identifiability conditions for the different variants of \emph{colBiSBM} and develop a variational EM algorithm for parameter estimation, coupled with an adaptation of the Integrated Classification Likelihood (ICL) criterion for model selection. We demonstrate how our approach can be used to classify networks based on their topology or organization. Simulation studies highlight the ability of \emph{colBiSBM} to recover common structures, improve clustering performance, and enhance link prediction by borrowing strength across networks. An application to plant--pollinator networks highlights how the method uncovers shared ecological roles and partitions networks into sub-collections with similar connectivity patterns. These results illustrate the methodological and practical advantages of joint modeling over separate network analyses in the study of bipartite systems.

Many online learning algorithms, including classical online PCA methods, enforce explicit normalization steps that discard the evolving norm of the parameter vector. We show that this norm can in fact encode meaningful information about the underlying statistical structure of the problem, and that exploiting this information leads to improved learning behavior. Motivated by this principle, we introduce Implicitly Normalized Online PCA (INO-PCA), an online PCA algorithm that removes the unit-norm constraint and instead allows the parameter norm to evolve dynamically through a simple regularized update. We prove that in the high-dimensional limit the joint empirical distribution of the estimate and the true component converges to a deterministic measure-valued process governed by a nonlinear PDE. This analysis reveals that the parameter norm obeys a closed-form ODE coupled with the cosine similarity, forming an internal state variable that regulates learning rate, stability, and sensitivity to signal-to-noise ratio (SNR). The resulting dynamics uncover a three-way relationship between the norm, SNR, and optimal step size, and expose a sharp phase transition in steady-state performance. Both theoretically and experimentally, we show that INO-PCA consistently outperforms Oja's algorithm and adapts rapidly in non-stationary environments. Overall, our results demonstrate that relaxing norm constraints can be a principled and effective way to encode and exploit problem-relevant information in online learning algorithms.

Differential privacy is increasingly formalized through the lens of hypothesis testing via the robust and interpretable $f$-DP framework, where privacy guarantees are encoded by a baseline Blackwell trade-off function $f_{\infty} = T(P_{\infty}, Q_{\infty})$ involving a pair of distributions $(P_{\infty}, Q_{\infty})$. The problem of choosing the right privacy metric in practice leads to a central question: what is a statistically appropriate baseline $f_{\infty}$ given some prior modeling assumptions? The special case of Gaussian differential privacy (GDP) showed that, under compositions of nearly perfect mechanisms, these trade-off functions exhibit a central limit behavior with a Gaussian limit experiment. Inspired by Le Cam's theory of limits of statistical experiments, we answer this question in full generality in an infinitely divisible setting. We show that suitable composition experiments $(P_n^{\otimes n}, Q_n^{\otimes n})$ converge to a binary limit experiment $(P_{\infty}, Q_{\infty})$ whose log-likelihood ratio $L = \log(dQ_{\infty} / dP_{\infty})$ is infinitely divisible under $P_{\infty}$. Thus any limiting trade-off function $f_{\infty}$ is determined by an infinitely divisible law $P_{\infty}$, characterized by its Levy--Khintchine triplet, and its Esscher tilt defined by $dQ_{\infty}(x) = e^{x} dP_{\infty}(x)$. This characterizes all limiting baseline trade-off functions $f_{\infty}$ arising from compositions of nearly perfect differentially private mechanisms. Our framework recovers GDP as the purely Gaussian case and yields explicit non-Gaussian limits, including Poisson examples. It also positively resolves the empirical $s^2 = 2k$ phenomenon observed in the GDP paper and provides an optimal mechanism for count statistics achieving asymmetric Poisson differential privacy.