The chef behind Wales' only two-Michelin-star restaurant has said he is not embarrassed after it was awarded a one-star hygiene rating. Ynyshir Restaurant and Rooms, near Machynlleth in Ceredigion, which charges nearly £500 per head, received the rating after a visit by food safety officers on 5 November. According to the Food Standards Agency (FSA), a score of one out of five means major improvement is necessary. But chef patron Gareth Ward, a contestant on MasterChef The Professionals, said the restaurant was working at the highest standard in the world and doing something different with how it approaches raw ingredients and techniques. Ynyshir offers a high-end dining experience starting at £468 per person, including a 30-course tasting menu and an in-house DJ.

We consider the widely-used average-linkage, single-linkage, and Ward's methods for computing hierarchical clusterings of high-dimensional Euclidean inputs. It is easy to show that there is no efficient implementation of these algorithms in high dimensional Euclidean space since it implicitly requires to solve the closest pair problem, a notoriously difficult problem. However, how fast can these algorithms be implemented if we allow approximation? More precisely: these algorithms successively merge the clusters that are at closest average (for average-linkage), minimum distance (for single-linkage), or inducing the least sum-of-square error (for Ward's). We ask whether one could obtain a significant running-time improvement if the algorithm can merge $\gamma$-approximate closest clusters (namely, clusters that are at distance (average, minimum, or sum-of-square error) at most $\gamma$ times the distance of the closest clusters). We show that one can indeed take advantage of the relaxation and compute the approximate hierarchical clustering tree using $\widetilde{O}(n)$ $\gamma$-approximate nearest neighbor queries.

The claim and evidence conflict pairs can be found at https://huggingface. The scope of our dataset is purely for scientific research. Conflict V erification: Ensuring that the default and conflict evidence are contradictory. The human evaluation results showed a high level of accuracy in our data generation process. We select models with 2B and 7B parameters for our analysis. MA2 [ Touvron et al., 2023 ] is a popular open-source foundation model, trained on 2T Models with 7B and 70B parameters are selected for our analysis. To facilitate parallel training, we employ DeepSpeed Zero-Stage 3 [ Ren et al., The prompt for generating semantic conflict descriptions is shown in Figure 1 . The prompt for generating default evidence is shown in Table 6 . The prompt for generating misinformation conflict evidence is shown in Table 7 . The prompt for generating temporal conflict evidence is shown in Table 8 . The prompt for generating semantic conflict evidence is shown in Table 9 .

We consider the widely-used average-linkage, single-linkage, and Ward's methods for computing hierarchical clusterings of high-dimensional Euclidean inputs. It is easy to show that there is no efficient implementation of these algorithms in high dimensional Euclidean space since it implicitly requires to solve the closest pair problem, a notoriously difficult problem. However, how fast can these algorithms be implemented if we allow approximation? More precisely: these algorithms successively merge the clusters that are at closest average (for average-linkage), minimum distance (for single-linkage), or inducing the least sum-of-square error (for Ward's). We ask whether one could obtain a significant running-time improvement if the algorithm can merge γ -approximate closest clusters (namely, clusters that are at distance (average, minimum, or sum-of-square error) at most γ times the distance of the closest clusters). We show that one can indeed take advantage of the relaxation and compute the approximate hierarchical clustering tree using r O pn q γ -approximate nearest neighbor queries.

Evaluating the reasoning ability of language models (LMs) is complicated by their extensive parametric world knowledge, where benchmark performance often reflects factual recall rather than genuine reasoning. Existing datasets and approaches (e.g., temporal filtering, paraphrasing, adversarial substitution) cannot cleanly separate the two. We present SynthWorlds, a framework that disentangles task reasoning complexity from factual knowledge. In SynthWorlds, we construct parallel corpora representing two worlds with identical interconnected structure: a real-mapped world, where models may exploit parametric knowledge, and a synthetic-mapped world, where such knowledge is meaningless. On top of these corpora, we design two mirrored tasks as case studies: multi-hop question answering and page navigation, which maintain equal reasoning difficulty across worlds. Experiments in parametric-only (e.g., closed-book QA) and knowledge-augmented (e.g., retrieval-augmented) LM settings reveal a persistent knowledge advantage gap, defined as the performance boost models gain from memorized parametric world knowledge. Knowledge acquisition and integration mechanisms reduce but do not eliminate this gap, highlighting opportunities for system improvements. Fully automatic and scalable, SynthWorlds provides a controlled environment for evaluating LMs in ways that were previously challenging, enabling precise and testable comparisons of reasoning and memorization.

The claim and evidence conflict pairs can be found at https://huggingface. The scope of our dataset is purely for scientific research. Conflict V erification: Ensuring that the default and conflict evidence are contradictory. The human evaluation results showed a high level of accuracy in our data generation process. We select models with 2B and 7B parameters for our analysis. MA2 [ Touvron et al., 2023 ] is a popular open-source foundation model, trained on 2T Models with 7B and 70B parameters are selected for our analysis. To facilitate parallel training, we employ DeepSpeed Zero-Stage 3 [ Ren et al., The prompt for generating semantic conflict descriptions is shown in Figure 1 . The prompt for generating default evidence is shown in Table 6 . The prompt for generating misinformation conflict evidence is shown in Table 7 . The prompt for generating temporal conflict evidence is shown in Table 8 . The prompt for generating semantic conflict evidence is shown in Table 9 .

Large language models (LLMs) have achieved impressive advancements across numerous disciplines, yet the critical issue of knowledge conflicts, a major source of hallucinations, has rarely been studied. While a few research explored the conflicts between the inherent knowledge of LLMs and the retrieved contextual knowledge, a comprehensive assessment of knowledge conflict in LLMs is still missing.

Urban greenery is often linked to better health, yet findings from past research have been inconsistent. One reason is that official greenery metrics measure the amount or nearness of greenery but ignore how often people actually may potentially see or use it in daily life. To address this gap, we introduced a new classification that separates on-road greenery, which people see while walking through streets, from off-road greenery, which requires planned visits. We did so by combining aerial imagery of Greater London and greenery data from OpenStreetMap with quantified greenery from over 100,000 Google Street View images and accessibility estimates based on 160,000 road segments. We linked these measures to 7.45 billion medical prescriptions issued by the National Health Service and processed through our methodology. These prescriptions cover five conditions: diabetes, hypertension, asthma, depression, and anxiety, as well as opioid use. As hypothesized, we found that green on-road was more strongly linked to better health than four widely used official measures. For example, hypertension prescriptions dropped by 3.68% in wards with on-road greenery above the median citywide level compared to those below it. If all below-median wards reached the citywide median in on-road greenery, prescription costs could fall by up to £3.15 million each year. These results suggest that greenery seen in daily life may be more relevant than public yet secluded greenery, and that official metrics commonly used in the literature have important limitations.

The availability of downstream resources plays is critical in planning the admission of elective surgery patients. The most crucial one is inpatient beds. To ensure bed availability, hospitals may use machine learning (ML) models to predict patients' length-of-stay (LOS) in the admission planning stage. However, the real value of the LOS for each patient may differ from the predicted one, potentially making the schedule infeasible. To address such infeasibilities, it is possible to implement rescheduling strategies that take advantage of operational flexibility. For example, planners may postpone admission dates, relocate patients to different wards, or even transfer patients who are already admitted among wards. A straightforward assumption is that better LOS predictions can help reduce the impact of rescheduling. However, the training process of ML models that can make such accurate predictions can be very costly. Building on previous work that proposed simulated ML for evaluating data-driven approaches, this paper explores the relationship between LOS prediction accuracy and rescheduling flexibility across various corrective policies. Specifically, we examine the most effective patient rescheduling strategies under LOS prediction errors to prevent bed overflows while optimizing resource utilization