We introduce a notion of equivariant vector bundles on schemes over semirings. We do this by considering the functor of points of a locally free sheaf. We prove that every toric vector bundle on a toric scheme X over an idempotent semifield equivariantly splits as a sum of toric line bundles. We then study the equivariant Picard group $\operatorname{Pic}_G(X)$. Finally, we prove a version of Klyachko’s classification theorem for toric vector bundles over an idempotent semifield.

Sharp, nonasymptotic bounds are obtained for the relative entropy between the distributions of sampling with and without replacement from an urn with balls of $c\geq 2$ colors. Our bounds are asymptotically tight in certain regimes and, unlike previous results, they depend on the number of balls of each color in the urn. The connection of these results with finite de Finetti-style theorems is explored, and it is observed that a sampling bound due to Stam (1978) combined with the convexity of relative entropy yield a new finite de Finetti bound in relative entropy, which achieves the optimal asymptotic convergence rate.

Is it ever rational to change your mind based on learning that others have changed theirs? This paper answers affirmatively and explores the conditions under which learning about others’ mind-changes should prompt you to reconsider your own. I propose that learning about others’ shifts in belief can motivate further inquiry, provide information about the existence or quality of first-order evidence, and recalibrate our evaluation of the issues at stake. However, not all changes of mind are epistemically meaningful: some may be superficial, misleading, or driven by non-epistemic factors. Critical evaluation is necessary for distinguishing between cases that provide genuine insight and those that are irrelevant. By investigating these dynamics, I aim to illuminate the broader epistemological significance of mind-changing and its implications for navigating complex and contentious issues.

The concept of hedging has been recently introduced and has been gaining traction in International Relations (IR) literature. So far, the notion has been mainly employed to make sense of the strategic behaviour of some south-east Asian secondary states amid growing Sino-American great power competition. Hedging can be understood as a strategy through which a minor state avoids clearly aligning vis-à-vis two powerful vying actors, maintaining instead an in-between and balanced position. As such, hedging can be interpreted as a peculiar form of neutrality. Yet such a paralleling has not been spelled out clearly from a theoretical standpoint in the existing literature. Moreover, no attempt has been made to precisely position hedging among the different categories of neutrality. This is a major gap, as it deprives the hedging concept of much of its theoretical and analytical usefulness in informing scholarly analyses. By precisely locating hedging within the neutrality family and by identifying its main analytical features, this paper aims to clarify theoretically the ‘nature’ of the phenomenon. At the same time, such operation aims to move the hedging literature beyond its current overwhelming focus on contemporary south-east Asia, opening up interesting empirical perspectives for the study of hedging across time.

Intestinal health challenges – including dysbiosis, inflammatory disorders, and pathogen susceptibility – impose severe economic losses and welfare concerns in intensive livestock production. Functional lipids, defined as bioactive lipid molecules with physiological benefits beyond basic nutrition, offer promising solutions to these issues. This review establishes a comprehensive definition of functional lipids and elucidates their metabolic process. Using short- and medium-chain fatty acid glycerides as a prime example, we examine their significant roles in energy homeostasis, gut microbiota composition and diversity, immune modulation, and antibacterial and antiviral activities. Additionally, we critically evaluate their current applications and future industrial potential in livestock production, providing evidence-based recommendations for their optimal implementation in animal nutrition strategies.

The COVID-19 pandemic brought the EU health mandate under unprecedented scrutiny, providing a new impetus for action. The European Commission launched the ‘European Health Union’ (EHU), bringing a number of pre-existing and newer policy initiatives under a common umbrella. This contribution looks back at the recent developments in EU health law and policy, taking the 2019–2024 parliamentary term as a boundary. It offers an overview of what the EHU currently is, and what it could become. Despite its potential, the EHU is not yet a game changer. This can only happen if changes are brought to the EU’s competence and budgetary frameworks. The contribution provides first a brief introduction to the EU’s complex health competence framework and its general policy orientations in the field. We turn next to COVID-19, offering a condensed overview of the EU’s response and of the subsequent changes brought to the legal framework applicable to health emergencies. We finish by casting a closer look at the EHU, examining the descriptive and normative aspects of this concept, and making recommendations to increase the clarity, quality and legitimacy of EU action in the field.

The ageing population is anticipated to encounter several challenges related to sustainability. While policies such as ageing in place can benefit older adults in terms of familiarity and independence, these policies can also lead to increased social isolation. To facilitate ageing in the right place, it is crucial to understand how the design of environments promotes social sustainability. This article presents a scoping review of empirical research focused on the characteristics of housing and surrounding environments that support social integration, cohesion and participation of older adults. The search strategy was conducted in five databases, resulting in 20,477 articles. After screening 7,550 titles and abstracts based on predetermined inclusion and exclusion criteria, 19 articles were selected. The findings of these articles are presented across three themes: (1) housing environments, (2) environments beyond the home and (3) the social environment. Although there is no one-size-fits-all housing model for older adults, the authors suggest that ageing in place policies should be reconceptualized as ageing in ‘places’ and ‘spaces’, emphasizing the diversity of social needs of older adults. Understanding the environmental characteristics, the role of accessible and safe environments beyond the home, and how people and culture support a sense of belonging provides a policy direction for how to design socially sustainable environments for older adults in the future.

The adoption of the main text of the Pandemic Agreement at the 2025 World Health Assembly is a milestone in global health law. The adopted text makes several key contributions, but there were several missed opportunities in the negotiating process, and key roadblocks remain for the future of the Pandemic Agreement.

This paper examines the legal implications of the explicit mentioning of automation bias (AB) in the Artificial Intelligence Act (AIA). The AIA mandates human oversight for high-risk AI systems and requires providers to enable awareness of AB, i.e., the human tendency to over-rely on AI outputs. The paper analyses the embedding of this extra-juridical concept in the AIA, the asymmetric division of responsibility between AI providers and deployers for mitigating AB, and the challenges of legally enforcing this novel awareness requirement. The analysis shows that the AIA’s focus on providers does not adequately address design and context as causes of AB, and questions whether the AIA should directly regulate the risk of AB rather than just mandating awareness. As the AIA’s approach requires a balance between legal mandates and behavioural science, the paper proposes that harmonised standards should reference the state of research on AB and human-AI interaction, holding both providers and deployers accountable. Ultimately, further empirical research on human-AI interaction will be essential for effective safeguards.

This study analyses the evolution of body mass index (BMI) as income increases across the population, controlling for age, sex, educational level, marital status and some lifestyle habits. To this end, a quantile regression, an econometric technique that readjusts the weights of the variables in each quantile to minimize deviations, has been carried out, where the variable that orders the sample is income. We use 316,777 observations from the European Health Interview Survey (EHIS) for these regressions. This approach allows us to separate the regression analyses for low-, middle-, and high-income groups, evidence that as individual income increases, BMI tends to rise. Consequently, individuals with higher incomes exhibit higher BMI levels. Additionally, the estimated parameters for explanatory variables increase with income, signifying that wealthier individuals not only have a greater likelihood of increased BMI but also that socio-economic factors influencing BMI – whether positively or negatively – evince a stronger impact as income levels rise.

Early language development has rarely been studied in hearing children with deaf parents who are exposed to both a spoken and a signed language (bimodal bilinguals). This study presents longitudinal data of early communication and vocabulary development in a group of 31 hearing infants exposed to British Sign Language (BSL) and spoken English, at 6 months, 15 months, 24 months and 7 years, in comparison with monolinguals (exposed to English) and unimodal bilinguals (exposed to two spoken languages). No differences were observed in early communication or vocabulary development between bimodal bilinguals and monolinguals, but greater early communicative skills in infancy were found in bimodal bilinguals compared to unimodal bilinguals. Within the bimodal bilingual group, BSL and English vocabulary sizes were positively related. These data provide a healthy picture of early language acquisition in those learning a spoken and signed language simultaneously from birth.

This study investigated the effects of enzyme and/or sodium butyrate supplementation on the performance, eggshell quality, pancreatic enzyme activities and jejunum histology of laying quails-fed diets containing sunflower meal (SFM). A total of 140 24-week-old quails were randomly allocated into five experimental groups with 14 replicates each. The treatment diets were: NC (negative control without SFM), PC (positive control with 25% SFM), PC+E (PC + 500 g/tonne multi-enzyme), PC+B (PC + 1000 g/tonne sodium butyrate) and PC+EB (PC + 500 g/tonne multi-enzyme + 1000 g/tonne sodium butyrate).

As a result of this study, egg production was significantly higher in PC, PC+E and PC+EB groups compared to NC, while feed intake increased in PC but decreased with enzyme and/or sodium butyrate supplementation. Eggshell-breaking strength was highest in PC+B, whereas eggshell ratio and thickness increased across all groups compared to NC. Pancreatic lipase activity increased in PC+E and PC+B, but pancreatic amylase and protease activities decreased in all treatments compared to NC. Villus height (VH) and crypt depth (CD) improved with enzyme and/or sodium butyrate supplementation, with villus width and surface area significantly greater in PC+E and PC+EB. However, the VH/CD ratio decreased in all groups except PC+EB. In conclusion, diets containing 25% SFM did not impair performance or egg quality and improved eggshell thickness and ratio. Enzyme and/or sodium butyrate supplementation reduced feed intake enhanced pancreatic lipase activity, decreased amylase and protease activities and improved jejunum histology, with sodium butyrate notably increasing eggshell-breaking strength.