Let a group Γ act on a paracompact, locally compact, Hausdorff space M by homeomorphisms and let 2M denote the set of closed subsets of M. We endow 2M with the Chabauty topology, which is compact and admits a natural Γ-action by homeomorphisms. We show that for every minimal Γ-invariant closed subset $\mathcal{Y}$ of 2M consisting of compact sets, the union $\bigcup \mathcal{Y}\subset M$ has compact closure.

As an application, we deduce that every compact uniformly recurrent subgroup of a locally compact group is contained in a compact normal subgroup. This generalizes a result of Ušakov on compact subgroups whose normalizer is compact.

This study discusses the intersection between Black/African Digital Humanities, and computational methods, including natural language processing (NLP) and generative artificial intelligence (AI). We have structured the narrative around four critical themes: biases in colonial archives; postcolonial digitization; linguistic and representational inequalities in Lusophone digital content; and technical limitations of AI models when applied to the archival records from Portuguese-colonized African territories (1640–1822). Through three case studies relating to the Africana Collection at the Arquivo Histórico Ultramarino, the Dembos Collection, and Sebestyén’s Caculo Cangola Collection, we demonstrate the infrastructural biases inherent in contemporary computational tools. This begins with the systematic underrepresentation of African archives in global digitization efforts and ends with biased AI models that have not been trained on African historical corpora.

This paper examines American public attitudes toward corrective measures against uncooperative security allies through a preregistered survey experiment on a nationally representative sample of 1,502 American citizens. The findings demonstrate strong public support for corrective measures, particularly coercive strategies such as economic sanctions and military aid reduction, against allies whose policies conflict with the dominant power’s interests. While alliance discord also triggers demands for reduced American contributions to the alliance, public response varies substantially based on the nature of the misalignment and the characteristics of the uncooperative ally. Notably, the ally regime type significantly moderates support for corrective measures, with Americans demonstrating marked reluctance to endorse punitive actions against democratic allies. However, neither the ally’s military capabilities nor the presence of formal treaty arrangements significantly moderates public preferences. These findings contribute to our understanding of alliance management and the domestic foundations of international cooperation while offering insights into the pressures leaders face when addressing alliance noncompliance.

Research finds genetic predisposition for depression is associated with increases in depression across adolescence and adulthood. In turn, depressive symptoms in adolescence are associated with substance use. However, there has been modest examination of genetic predisposition for depression, growth in depressive symptoms, and substance use from late childhood through adolescence, and mostly in White samples. Also, psychosocial interventions can attenuate associations between genetic predisposition and psychopathology, a genotype by intervention (GxI) effect. We examined associations among polygenic risk for depression, growth in depressive symptoms from age 7 to 16, and substance use at age 16, as well as moderation by a family-based preventive intervention. Participants were African-ancestry (n = 154) and European-ancestry (n = 219) youth from the Early Steps Multisite Study, half of whom participated in the Family Check-Up intervention. A small polygenic by intervention effect was found on reductions in depressive symptoms for African-ancestry youth, and growth in depressive symptoms was positively associated with substance use at age 16. In sensitivity analyses, a small GxI effect was detected in European-ancestry youth on reductions in depressive symptom slopes from age 10 to 16. These findings highlight how early intervention can buffer genetic effects on depressive symptoms over time.

Observed competitive market profit margins in property and casualty insurance have typically been higher than the capital assets pricing model adjustment for risky loss cashflows would suggest. Explanations for this difference include frictions from operating an insurance business and capital risks that are not adequately recognised and rewarded by the theory. It is proposed that the difference may instead be related to the consumption of insurance services and claim fulfilment with an additional fair profit margin evaluated using marginal utility pricing principles.

While increasing seafood consumption may help address micronutrient deficiencies and metabolic disorders, evidence supporting this recommendation in the Indian context remains limited and inconclusive. Using the nationally representative cross-sectional 2019–2021 National Family Health Survey dataset, we investigated the association of fish consumption frequency with anaemia and metabolic disorders (overweight/obesity, hypertension and hyperglycaemia) among adult men (aged 15–54 years) and women (aged 15–49 years) in India. A control function (CF) method was employed to examine the association in individuals who consumed fish daily and those who reported consuming fish daily/weekly. The analysis was restricted to non-vegetarians (who reported ever consuming egg, fish or meat). Overall, 86·9 % of men and 74·7 % of women were non-vegetarians. CF analysis revealed that both daily and daily/weekly fish consumption were associated with a reduced risk of anaemia among both men and women. Daily fish consumers exhibited increased likelihood of overweight/obesity (men: β: 0·405, 95 % CI: 0·074, 0·735, P: 0·017; women: β: 0·248, 95 % CI 0·125, 0·370, P < 0·001). Conversely, daily/weekly fish intake was associated with a reduced risk of overweight/obesity in men (β: −0·041, 95 % CI: −0·069, −0·013; P: 0·004). Daily/weekly fish consumption was associated with a reduced risk of hypertension and increased odds of hyperglycaemia among men. Fish consumption demonstrated a potentially protective relationship against hypertension in women, regardless of how often they consumed fish, while also being associated with a higher prevalence of hyperglycaemia. Indian adults can improve their health by eating more fish, which can help fight anaemia and may also reduce overweight/obesity and high blood pressure.

Complete exploration of design spaces is often computationally prohibitive. Classical search methods offer a solution but are limited by challenges like local optima and an inability to traverse dislocated design spaces. Quantum computing (QC) offers a potential solution by leveraging quantum phenomena to achieve computational speed-ups. However, the practical capability of current QC platforms to deliver these advantages remains unclear. To investigate this, we apply and compare two quantum approaches – the Gate-Based Grover’s algorithm and quantum annealing (QA) – to a generic tile placement problem. We benchmark their performance on real quantum hardware (IBM and D-Wave, respectively) against a classical brute-force search. QA on D-Wave’s hardware successfully produced usable results, significantly outperforming a classical brute-force approach (0.137 s vs 14.8 s) at the largest scale tested. Conversely, Grover’s algorithm on IBM’s gate-based hardware was dominated by noise and failed to yield solutions. While successful, the QA results exhibited a hardware-induced bias, where equally optimal solutions were not returned with the same probability (coefficient of variation: 0.248–0.463). These findings suggest that for near-term engineering applications, QA shows more immediate promise than current gate-based systems. This study’s contribution is a direct comparison of two physically implemented quantum approaches, offering practical insights, reformulation examples and clear recommendations on the utilisation of QC in engineering design.

Understanding the formation and evolution of fast flowing ice streams is essential to projecting the response of ice sheets to climate forcings. Slow-flowing or stagnant ice streams can slide at low velocities over a bed that is below the bulk melting point of ice, dissipating small amounts of frictional heat. This subtemperate sliding complicates the assumed dichotomy between frozen and thawed beds embedded in many large-scale ice sheet models. In this study, we allow for subtemperate sliding in a simple ice stream box model. This leads to non-negligible frictional heat dissipation, which can accelerate sliding and lead to runaway acceleration of stagnant ice streams. These results suggest that subtemperate sliding and the associated thermo-frictional feedback are important control on ice stream temporal variability over longer timescales characterizing Heinrich events. In addition, subtemperate sliding is likely an important physical process to consider in modeling the potential reactivation of stagnant ice streams like Kamb Ice Stream, which evolve on shorter centennial timescales.

Like many newer EU Free Trade Agreements, the Trade and Cooperation Agreement (TCA) includes commitments concerning labour and social standards and environment and climate policy under the title the ‘Level Playing Field’. This title includes non-regression provisions, which prohibit reducing or weakening certain standards ‘in a manner affecting trade’, and novel rebalancing provisions, which allow the parties to take unilateral measures if material impacts on trade are arising as a result of significant divergences in levels of protection in specific areas of regulation. Although terminology linking trade to labour and environmental issues is becoming reasonably common in trade agreements, there has only been limited consideration as to what trade effects or impacts actually need to be demonstrated. This paper argues that the language of ‘manner affecting trade’ and ‘material impact on trade’ in the TCA denotes a ‘conditions of competition’ test as opposed to a stricter, and relatively more difficult to satisfy, trade remedies model. It further considers the possible application of the provisions in the context of the UK’s 2022 strikes measures, highlighting that even if a conditions of competition test is used, there are serious questions as to whether the non-regression and rebalancing provisions in the TCA are efficacious in achieving values-based objectives.

We give a construction of integral local Shimura varieties which are formal schemes that generalise the well-known integral models of the Drinfeld p-adic upper half spaces. The construction applies to all classical groups, at least for odd p. These formal schemes also generalise the formal schemes defined by Rapoport-Zink via moduli of p-divisible groups, and are characterised purely in group-theoretic terms.

More precisely, for a local p-adic Shimura datum $(G, b, \mu)$ and a quasi-parahoric group scheme ${\mathcal {G}} $ for G, Scholze has defined a functor on perfectoid spaces which parametrises p-adic shtukas. He conjectured that this functor is representable by a normal formal scheme which is locally formally of finite type and flat over $O_{\breve E}$. Scholze-Weinstein proved this conjecture when $(G, b, \mu)$ is of (P)EL type by using Rapoport-Zink formal schemes. We prove this conjecture for any $(G, \mu)$ of abelian type when $p\neq 2$, and when $p=2$ and G is of type A or C. We also relate the generic fibre of this formal scheme to the local Shimura variety, a rigid-analytic space attached by Scholze to $(G, b, \mu , {\mathcal {G}})$.

Sheath-ends are poorly represented in works regarding weaponry of the Cimmerian period (10th–7th century BC), despite forming an important component, particularly among the melee weapons of the time. There are several reasons for this neglect: until recently, the number of known sheath-ends was quite small, thus making it impossible to speak of types, variants or cultural affiliations; also, most of the previously published sheath-ends are spread over a large territory and were published many decades ago. Therefore, some of them may be unknown to researchers due to the age of publications, as well as linguistic and cultural barriers. Over the past few years, a larger number of new sheath-ends has emerged. Some of them belong to previously known types, others are completely new. Their analysis is here conducted using the comparative method. The total number of sheath-ends now known makes it possible to begin a discussion about their types, chronology and origins, which will undoubtedly develop as new finds appear.

This study demonstrated the incidences of hospital-acquired colonization by extended-spectrum beta-lactamase-producing Enterobacterales (ESBL-E), carbapenem-resistant Enterobacterales (CRE), and vancomycin-resistant enterococci (VRE) of 22%, 8%, and 8% among hematologic malignancy patients. Difference in time to colonization detection between VRE (14 d) and ESBL-E and CRE (7 d) may inform appropriate surveillance measures.

In p-adic Hodge theory and the p-adic Langlands program, Banach spaces with $\mathbf {Q}_p$-coefficients and p-adic Lie group actions are central. Studying the subrepresentation of G-locally analytic vectors, $W^{\mathrm {la}}$, is useful because $W^{\mathrm {la}}$ can be studied via the Lie algebra $\mathrm {Lie}(G)$, which simplifies the action of G. Additionally, $W^{\mathrm {la}}$ often behaves as a decompletion of W, making it closer to an algebraic or geometric object.

This article introduces a notion of locally analytic vectors for W in a mixed characteristic setting, specifically for $\mathbf {Z}_p$-Tate algebras. This generalization encompasses the classical definition and also specializes to super-Hölder vectors in characteristic p. Using binomial expansions instead of Taylor series, this new definition bridges locally analytic vectors in characteristic $0$ and characteristic p.

Our main theorem shows that under certain conditions, the map $W \mapsto W^{\mathrm {la}}$ acts as a descent, and the derived locally analytic vectors $\mathrm {R}_{\mathrm {la}}^i(W)$ vanish for $i \geq 1$. This result extends Theorem C of [Por24], providing new tools for propagating information about locally analytic vectors from characteristic $0$ to characteristic p.

We provide three applications: a new proof of Berger-Rozensztajn’s main result using characteristic $0$ methods, the introduction of an integral multivariable ring $\widetilde {\mathbf {A}}_{\mathrm {LT}}^{\dagger ,\mathrm {la}}$ in the Lubin-Tate setting, and a novel interpretation of the classical Cohen ring $\mathbf {{A}}_{\mathbf {Q}_p}$ from the theory of $(\varphi ,\Gamma )$-modules in terms of locally analytic vectors.

Recently, autonomous aerial systems have received unparalleled popularity and applications as varied as they are innovative in the civil domain. The unmanned aerial vehicle (UAV) is now the subject of intensive research in both aeronautical and automotive engineering.

This paper presents a new, robust gain-scheduled adaptive control strategy for a class of UAV with linear parameter varying (LPV) models. The proposed controller synthesis involves a set of pre-tuned linear quadratic regulator (LQR) combined with fractional-order PID controllers supervised with an adaptive switching law. The main innovation in this work is the enhancement of the classical gain-scheduling adaptive control robustness for systems with LPV models by combining a set of robust LQR + fractional-order PID compensators. The stability of the resulting controller is demonstrated and its efficiency is validated using a numerical simulation example on a civilian UAV system airspeed and altitude control to illustrate its practical efficiency and achieved robustness.