Can Ukraine restore its pre-war borders? Why are Tomahawk missiles for Ukraine a'red line' for Russia? Is Russia testing NATO with aerial incursions in Europe? Russian war correspondent Ivan Zuyev has been killed by a Ukrainian drone strike while on assignment on the front line of the war in southern Ukraine's Zaporizhia region, his publication, state news agency RIA said. Zuyev's colleague, Yuri Voitkevich, was seriously wounded in the attack.

Taylor Swift fans are driving a surge in popularity of a German museum exhibiting a portrait of the Shakespeare character Ophelia, recently reimagined in a song and music video from Swift's new album The Life of a Showgirl. The Hessische Landesmuseum in the central German city of Wiesbaden saw hundreds more visitors than usual over the weekend, as fans hoped to see the real version of the painting that opens the music video for The Fate of Ophelia. In the video, viewed more than 65 million times on Youtube, the painting comes alive, with Swift at its centre. We're really enjoying this attention - it's a lot of fun, museum spokesperson Susanne Hirschmann told the Associated Press. Hirschmann said that one family had travelled from the northern city of Hamburg, a five-hour drive away, while some of the visitors were Americans from an army base nearby.

China's biggest shopping event starts five weeks early to revive spending It's known to be China's biggest online shopping event - taking place on 11 November each year. But this year, Single's Day sales have already begun in mid-October, as part of efforts by Chinese retailers to boost spending in a sluggish market. China has been plagued with issues like growing youth unemployment, a prolonged property crisis, steep government debt and an ongoing trade war with the US - all of which is making the country's consumers cut back on spending. The Chinese government has been spending billions - through family subsidies, more wages and discounts for consumer goods in a bid to counter this, but retail sales growth is still failing to meet expectations. Originally created by Alibaba as a Chinese shopping festival, Singles' Day is akin to Amazon's Prime Day or Black Friday promotions elsewhere in the world.

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Simulation-based inference (SBI) is emerging as a new statistical paradigm for addressing complex scientific inference problems. By leveraging the representational power of deep neural networks, SBI can extract the most informative simulation features for the parameters of interest. Sequential SBI methods extend this approach by iteratively steering the simulation process towards the most relevant regions of parameter space. This is typically implemented through an algorithmic structure, in which simulation and network training alternate over multiple rounds. This strategy is particularly well suited for high-precision inference in high-dimensional settings, which are commonplace in physics applications with growing data volumes and increasing model fidelity. Here, we introduce dynamic SBI, which implements the core ideas of sequential methods in a round-free, asynchronous, and highly parallelisable manner. At its core is an adaptive dataset that is iteratively transformed during inference to resemble the target observation. Simulation and training proceed in parallel: trained networks are used both to filter out simulations incompatible with the data and to propose new, more promising ones. Compared to round-based sequential methods, this asynchronous structure can significantly reduce simulation costs and training overhead. We demonstrate that dynamic SBI achieves significant improvements in simulation and training efficiency while maintaining inference performance. We further validate our framework on two challenging astrophysical inference tasks: characterising the stochastic gravitational wave background and analysing strong gravitational lensing systems. Overall, this work presents a flexible and efficient new paradigm for sequential SBI.

Selecting the latent dimensions (ranks) in tensor factorization is a central challenge that often relies on heuristic methods. This paper introduces a rigorous approach to determine rank identifiability in probabilistic tensor models, based on prior predictive moment matching. We transform a set of moment matching conditions into a log-linear system of equations in terms of marginal moments, prior hyperparameters, and ranks; establishing an equivalence between rank identifiability and the solvability of such system. We apply this framework to four foundational tensor-models, demonstrating that the linear structure of the PARAFAC/CP model, the chain structure of the Tensor Train model, and the closed-loop structure of the Tensor Ring model yield solvable systems, making their ranks identifiable. In contrast, we prove that the symmetric topology of the Tucker model leads to an underdetermined system, rendering the ranks unidentifiable by this method. For the identifiable models, we derive explicit closed-form rank estimators based on the moments of observed data only. We empirically validate these estimators and evaluate the robustness of the proposal.

In this paper we develop a deforestation detection pipeline that incorporates optical and Synthetic Aperture Radar (SAR) data. A crucial component of the pipeline is the construction of anomaly maps of the optical data, which is done using the residual space of a discrete Karhunen-Loève (KL) expansion. Anomalies are quantified using a concentration bound on the distribution of the residual components for the nominal state of the forest. This bound does not require prior knowledge on the distribution of the data. This is in contrast to statistical parametric methods that assume knowledge of the data distribution, an impractical assumption that is especially infeasible for high dimensional data such as ours. Once the optical anomaly maps are computed they are combined with SAR data, and the state of the forest is classified by using a Hidden Markov Model (HMM). We test our approach with Sentinel-1 (SAR) and Sentinel-2 (Optical) data on a $92.19\,km \times 91.80\,km$ region in the Amazon forest. The results show that both the hybrid optical-radar and optical only methods achieve high accuracy that is superior to the recent state-of-the-art hybrid method. Moreover, the hybrid method is significantly more robust in the case of sparse optical data that are common in highly cloudy regions.

Consider two sets of entities and their members' mutual affinity values, say drug-target affinities (DTA). Drugs and targets are said to interact in their effects on DTAs if drug's effect on it depends on the target. Presence of interaction implies that assigning a drug to a target and another drug to another target does not provide the same aggregate DTA as the reversed assignment would provide. Accordingly, correctly capturing interactions enables better decision-making, for example, in allocation of limited numbers of drug doses to their best matching targets. Learning to predict DTAs is popularly done from either solely from known DTAs or together with side information on the entities, such as chemical structures of drugs and targets. In this paper, we introduce interaction directions' prediction performance estimator we call interaction concordance index (IC-index), for both fixed predictors and machine learning algorithms aimed for inferring them. IC-index complements the popularly used DTA prediction performance estimators by evaluating the ratio of correctly predicted directions of interaction effects in data. First, we show the invariance of IC-index on predictors unable to capture interactions. Secondly, we show that learning algorithm's permutation equivariance regarding drug and target identities implies its inability to capture interactions when either drug, target or both are unseen during training. In practical applications, this equivariance is remedied via incorporation of appropriate side information on drugs and targets. We make a comprehensive empirical evaluation over several biomedical interaction data sets with various state-of-the-art machine learning algorithms. The experiments demonstrate how different types of affinity strength prediction methods perform in terms of IC-index complementing existing prediction performance estimators.

Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or uncertainty estimates, making them unreliable for practical use. We propose the Guess2Graph (G2G) framework, which uses expert guesses to guide the sequence of statistical tests rather than replacing them. This maintains statistical consistency while enabling performance improvements. We develop two instantiations of G2G: PC-Guess, which augments the PC algorithm, and gPC-Guess, a learning-augmented variant designed to better leverage high-quality expert input. Theoretically, both preserve correctness regardless of expert error, with gPC-Guess provably outperforming its non-augmented counterpart in finite samples when experts are "better than random."

Causal learning is the cognitive process of developing the capability of making causal inferences based on available information, often guided by normative principles. This process is prone to errors and biases, such as the illusion of causality, in which people perceive a causal relationship between two variables despite lacking supporting evidence. This cognitive bias has been proposed to underlie many societal problems, including social prejudice, stereotype formation, misinformation, and superstitious thinking. In this work, we examine whether large language models are prone to developing causal illusions when faced with a classic cognitive science paradigm: the contingency judgment task. To investigate this, we constructed a dataset of 1,000 null contingency scenarios (in which the available information is not sufficient to establish a causal relationship between variables) within medical contexts and prompted LLMs to evaluate the effectiveness of potential causes. Our findings show that all evaluated models systematically inferred unwarranted causal relationships, revealing a strong susceptibility to the illusion of causality. While there is ongoing debate about whether LLMs genuinely understand causality or merely reproduce causal language without true comprehension, our findings support the latter hypothesis and raise concerns about the use of language models in domains where accurate causal reasoning is essential for informed decision-making.