Predicting a complete spatially correlated field from sparse observations is a fundamental challenge in spatial statistics and environmental modelling. Classical interpolation methods such as Kriging rely on Gaussian process assumptions and variography, which can limit their effectiveness in non-stationary settings and require substantial domain expertise. In this work, we leverage an architecture based on convolutional neural networks (CNNs) for spatial interpolation that is trained and applied on a single partially observed field, without access to external data or prior fields. The model is supervised directly on the observed locations and learns to predict values at unobserved points on the user defined grid. Unlike Kriging, our method does not require explicit covariance modelling or variogram estimation, and it can flexibly capture local spatial patterns in a data-driven manner. This work demonstrates the potential of CNNs for single-instance spatial interpolation under sparse supervision, offering a practical alternative to classical geostatistical methods, and extending the use of CNNs to a new problem domain.

A French woman and her partner will remain in custody after allegedly abandoning her two young boys on a roadside in the south of Portugal, a court has ruled. The boys were found on Tuesday evening crying beside a road near Alcacer do Sal, about 100km (60 miles) south of Lisbon. The woman and her partner, identified by authorities as Marine R and Marc B, were arrested in Fatima on Thursday. As they were being led into court on Saturday morning, the man shouted I love you in French and the boys' mother sang. A judge subsequently ordered the pair be placed in pre-trial detention, French and Portuguese media report.

RoboCup is an international competition that promotes and advances robotics and AI through the challenges presented by its various leagues. We got the chance to sit down with Professor Manuela Veloso, one of RoboCup's founders, to find out more about how it all started, how the community has grown over the years, and the vision for the future. I think it would be very interesting to go right back to the beginning and hear how RoboCup got started. What was the initial idea, and how did it get set up? So we are talking about the mid-90s. In terms of the research in those days, it was the beginning of the internet and many AI and computer science researchers were focused on the internet, first on sophisticated search algorithms, on natural language understanding, on information retrieval, and then on software agents and machine learning applied to digital information. From what I recall, there was a smaller group of researchers who were interested in actual, physical robots, and in particular in AI and robotics.

As deep neural networks are deployed in safety-critical domains such as autonomous driving and medical diagnosis, stakeholders need explanations that are interpretable but also trustworthy with formal guarantees. Existing XAI methods fall short: heuristic attribution techniques (e.g., LIME, Integrated Gradients) highlight influential features but offer no mathematical guarantees about decision boundaries, while formal methods verify robustness yet remain untargeted, analyzing the nearest boundary regardless of whether it represents a critical risk. In safety-critical systems, not all misclassifications carry equal consequences; confusing a "Stop" sign for a "60 kph" sign is far more dangerous than confusing it with a "No Passing" sign. We introduce ViTaX (Verified and Targeted Explanations), a formal XAI framework that generates targeted semifactual explanations with mathematical guarantees. For a given input (class y) and a user-specified critical alternative (class t), ViTaX: (1) identifies the minimal feature subset most sensitive to the y->t transition, and (2) applies formal reachability analysis to guarantee that perturbing these features by epsilon cannot flip the classification to t. We formalize this through Targeted epsilon-Robustness, certifying whether a feature subset remains robust under perturbation toward a specific target class. ViTaX is the first method to provide formally guaranteed explanations of a model's resilience against user-identified alternatives. Evaluations on MNIST, GTSRB, EMNIST, and TaxiNet demonstrate over 30% fidelity improvement with minimal explanation cardinality.

Background: Single-cell RNA sequencing (scRNA-seq) enables gene expression profiling at cellular resolution but is inherently affected by sparsity caused by dropout events, where expressed genes are recorded as zeros due to technical limitations. These artifacts distort gene expression distributions and compromise downstream analyses. Numerous imputation methods have been proposed to recover latent transcriptional signals. These methods range from traditional statistical models to deep learning (DL)-based methods. However, their comparative performance remains unclear, as existing benchmarks evaluate only a limited subset of methods, datasets, and downstream analyses. Results: We present a comprehensive benchmark of 15 scRNA-seq imputation methods spanning 7 methodological categories, including traditional and DL-based methods. Methods are evaluated across 30 datasets from 10 experimental protocols on 6 downstream analyses. Results show that traditional methods, such as model-based, smoothing-based, and low-rank matrix-based methods, generally outperform DL-based methods, including diffusion-based, GAN-based, GNN-based, and autoencoder-based methods. In addition, strong performance in numerical gene expression recovery does not necessarily translate into improved biological interpretability in downstream analyses, including cell clustering, differential expression analysis, marker gene analysis, trajectory analysis, and cell type annotation. Furthermore, method performance varies substantially across datasets, protocols, and downstream analyses, with no single method consistently outperforming others. Conclusions: Our findings provide practical guidance for selecting imputation methods tailored to specific analytical objectives and underscore the importance of task-specific evaluation when assessing imputation performance in scRNA-seq data analysis.

In optimization problems, some variable subsets may have a joint non-linear or non-monotonical influence on the function value. Therefore, knowledge of variable dependencies may be crucial for effective optimization, and many state-of-the-art optimizers leverage it to improve performance. However, some real-world problem instances may be the subject of noise of various origins. In such a case, variable dependencies relevant to optimization may be hard or impossible to tell using dependency checks sufficient for problems without noise, making highly effective operators, e.g., Partition Crossover (PX), useless. Therefore, we use Statistical Linkage Learning (SLL) to decompose problems with noise and propose a new SLL-dedicated mask construction algorithm. We prove that if the quality of the SLL-based decomposition is sufficiently high, the proposed clustering algorithm yields masks equivalent to PX masks for the noise-free instances. The experiments show that the optimizer using the proposed mechanisms remains equally effective despite the noise level and outperforms state-of-the-art optimizers for the problems with high noise.

Artificial intelligence (AI) is moving increasingly beyond prediction to support decisions in complex, uncertain, and dynamic environments. This shift creates a natural intersection with operations research and management sciences (OR/MS), which have long offered conceptual and methodological foundations for sequential decision-making under uncertainty. At the same time, recent advances in deep learning, including feedforward neural networks, LSTMs, transformers, and deep reinforcement learning, have expanded the scope of data-driven modeling and opened new possibilities for large-scale decision systems. This tutorial presents an OR/MS-centered perspective on deep learning for sequential decision-making under uncertainty. Its central premise is that deep learning is valuable not as a replacement for optimization, but as a complement to it. Deep learning brings adaptability and scalable approximation, whereas OR/MS provides the structural rigor needed to represent constraints, recourse, and uncertainty. The tutorial reviews key decision-making foundations, connects them to the major neural architectures in modern AI, and discusses leading approaches to integrating learning and optimization. It also highlights emerging impact in domains such as supply chains, healthcare and epidemic response, agriculture, energy, and autonomous operations. More broadly, it frames these developments as part of a wider transition from predictive AI toward decision-capable AI and highlights the role of OR/MS in shaping the next generation of integrated learning--optimization systems.

The world's most family-friendly landmarks revealed - with six UK spots making the top 50 The UK's best staycations revealed by Daily Mail Travel - from a Gara Rock beach proposal to an £80-a-night mansion retreat This sun-drenched European coast offers great value - and it's just a two-hour flight away Don't get caught out by Ryanair's small bag restrictions - I've tested the carry-on suitcases and underseat bags that beat the strict requirements Why heading to Salcombe, one of Britain's most expensive seaside towns, in the shoulder season is an off-peak treat - and what to do there Tired of fun! Middle class families who turn their noses up at Butlin's are missing out Luxury hotel owner in Cornwall offers to foot British tourists' petrol bills to ease financial pain of staycation With flights disrupted amid Iran war, these are Europe's easiest countries to navigate by train - and how it compares to flying for price and time How to retire to the seaside for as little as £90,000 - and Britain's best hidden beach home spots New business class seats with IMAX-style wrap-around screens revealed - making passengers feel like they're in the cinema How the cost of your staycation REALLY compares with a'cheap' holiday abroad - when you factor in everything from food to fuel Why the Lake District shouldn't introduce tourism tax, says Cumbria tourism boss How Marseille became Europe's Capital of Cool - with 20 degree sunshine, sea views and amazing seafood The world's best food markets revealed - and a UK spot comes in second place READ MORE: The best hotels in the UK for 2026 revealed - does YOUR favourite make the list? Ready to hit the mute button on reality? Deep in the Pembrokeshire countryside lies a cosmic retreat that feels almost light years away from Earth. The awe-inspiring Spodnic UFO is one of three standout stays at Melin Mabes, a four-acre glamping site owned and ran by Martin Johnson and his wife, CarolAnne. 'It looks like it's just landed from outer space and aliens could come out,' Martin notes as he showcases his brainchild during the first episode of Channel's World's Most Secret Hotels.

We initiate the study of language generation in the limit, a model recently introduced by Kleinberg and Mullainathan [KM24], under the constraint of differential privacy. We consider the continual release model, where a generator must eventually output a stream of valid strings while protecting the privacy of the entire input sequence. Our first main result is that for countable collections of languages, privacy comes at no qualitative cost: we provide an $\varepsilon$-differentially-private algorithm that generates in the limit from any countable collection. This stands in contrast to many learning settings where privacy renders learnability impossible. However, privacy does impose a quantitative cost: there are finite collections of size $k$ for which uniform private generation requires $Ω(k/\varepsilon)$ samples, whereas just one sample suffices non-privately. We then turn to the harder problem of language identification in the limit. Here, we show that privacy creates fundamental barriers. We prove that no $\varepsilon$-DP algorithm can identify a collection containing two languages with an infinite intersection and a finite set difference, a condition far stronger than the classical non-private characterization of identification. Next, we turn to the stochastic setting where the sample strings are sampled i.i.d. from a distribution (instead of being generated by an adversary). Here, we show that private identification is possible if and only if the collection is identifiable in the adversarial model. Together, our results establish new dimensions along which generation and identification differ and, for identification, a separation between adversarial and stochastic settings induced by privacy constraints.