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.

William Inge, Edward Gordon Selwyn, and Charles Gore represent three Anglican responses to John Henry Newman’s Essay on the Development of Doctrine. Development sought to account for doctrinal changes in Christianity by characterising Christianity as a ‘real idea’, expressing an object in the mind that can only be shown in its fullness by encounters with different philosophies over time. This was part of a wider intellectual movement in the 19th century away from static ideas of doctrinal history and towards more dynamic and subjective treatments. Inge, Selwyn, and Gore all make use of Newman after the First World War. Inge argues Newman abstracts historical facts from their realities, and abandons the old concept of tradition, where the church is the custodian of revelation, in favour of a relativistic concept, new in each generation. Selwyn makes use of Newman’s idea to argue for the autonomy of religious experience as a source of human knowledge mediated through religious traditions. Gore argues Newman enables ‘mobility’ in communicating Christianity to different cultures but argues development can be used justify distortions of the first revelation. The test of their authenticity should be whether they are inclusive of those Christ would be inclusive.

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.

Soil respiration is the second largest natural flux of Carbon (C) between terrestrial ecosystems and the atmosphere, with tropical forests amongst the largest contributors to such soil-derived C effluxes. With climate change expected to drive changes in both temperature and rainfall, our ability to predict responses of the C cycle in the future hinges upon an understanding of how these factors influence soil respiration. However, these relationships remain poorly characterised across the seasonal tropics, especially South Asia. Here, for two seasonal tropical sites in the Western Ghats of India, we characterised annual, seasonal and temporal variation in soil respiration and assessed its temperature and moisture sensitivity over six years. At both sites, soil respiration was positively correlated with temperature at the instantaneous scale, but showed no relationship with temperature at seasonal or annual scales. In contrast, soil respiration showed significant relationships with rainfall and soil moisture at all temporal scales. At the annual scale, soil respiration was negatively correlated with total annual rainfall. At the seasonal scale, wet season Rs was significantly lower than in the dry season. At the instantaneous scale, Rs showed a parabolic relationship with soil moisture, where soil respiration increased with soil moisture up to ∼21 cm3cm-3 and decreased beyond that point. Our results suggest that future changes in the Indian summer monsoon, especially the frequency and intensity of extreme rainfall events, are likely to significantly impact soil respiration rates in this seasonal tropical forest.

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.

This study investigated the cylindrically divergent Rayleigh–Taylor instability (RTI) on a liquid–gas interface and its dependence on initial conditions. A novel hydrophobic technique was developed to generate a two-dimensional water–air interface with controlled initial conditions. The experimental configuration utilised high-pressure air injection to produce uniform circumferential acceleration. Amplitude measurements over time revealed that the cylindrical RTI growth depends strongly on the azimuthal wavenumber. Experimental results demonstrated that surface tension significantly suppresses the liquid–gas cylindrical RTI, even inducing a freeze-out and oscillatory perturbation growth – a phenomenon observed for the first time. Spectrum analysis of the interface contours demonstrated that the cylindrical RTI evolves in a weakly nonlinear regime. Linear and weakly nonlinear models were derived to accurately predict the time-varying interface amplitudes and high-order modes. The linear model was further used to determine conditions for unstable, freeze-out and oscillatory solutions of the cylindrically divergent RTI. These findings offer valuable insights into manipulating hydrodynamic instabilities in contracting/expanding geometries using surface tension.

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.

For an even positive integer n, we study rank-one Eisenstein cohomology of the split orthogonal group $\mathrm {O}(2n+2)$ over a totally real number field $F.$ This is used to prove a rationality result for the ratios of successive critical values of degree-$2n$ Langlands L-functions associated to the group $\mathrm {GL}_1 \times \mathrm {O}(2n)$ over F. The case $n=2$ specializes to classical results of Shimura on the special values of Rankin–Selberg L-functions attached to a pair of Hilbert modular forms.

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.

Let $(\phi _t)$ be a continuous semigroup of holomorphic functions in the unit disk. We prove that all its orbits are rectifiable and that its forward orbits are Lipschitz curves. Moreover, we find a necessary and sufficient condition in terms of hyperbolic geometry so that a backward orbit is a Lipschitz curve. We further explore the Lipschitz condition for forward orbits lying on the unit circle and then for semigroups of holomorphic functions in general simply connected domains.