For a complete discrete valuation field K, we show that one may always glue a separated formal algebraic space $\mathfrak {X}$ over $\mathcal {O}_K$ to a separated algebraic space U over K along an open immersion of rigid spaces $j\colon \mathfrak {X}^{\mathrm {rig}}\to U^{\mathrm {an}}$, producing a separated algebraic space X over $\mathcal {O}_K$. This process gives rise to an equivalence between such ‘gluing triples’ $(U,\mathfrak {X},j)$ and separated algebraic spaces X over $\mathcal {O}_K$, which one might interpret as a version of the Beauville–Laszlo theorem for algebraic spaces rather than coherent sheaves. Moreover, an analogous equivalence exists over any excellent base. Examples due to Matsumoto imply that the result of such a gluing might be a genuine algebraic space (not a scheme) even if U and the special fibre of $\mathfrak {X}$ are projective. The proof is a combination of the Nagata compactification theorem for algebraic spaces and of Artin’s contraction theorem. We give multiple examples and applications of this idea.

Clinical and translational science faces persistent challenges in public trust, effective communication, and siloed knowledge structures. Addressing these issues requires innovative educational and engagement strategies. We present an artist-in-residency program immersed into an undergraduate pathway program to integrate artwork as a tool to enhance science communication, foster public engagement, and build a resilient translational science workforce. Through structured art-science–community interactions, this initiative demonstrates how artistic practice builds a new collaborative communication framework for linking early-career scientists, clinical translational research faculty, and the broader community. The conceptual novelty of our science-art initiative promises to break communication barriers, increase public trust, and develop new, accessible science narratives.

Responding to our shared concern about the plight of the Bunya tree (Araucaria bidwillii) due to dieback caused by soil-borne pathogens, this composite article brings together narrative reflections from eight contributors, who respond to prompts on confronting dieback through their unique lived experiences and professional practices. The responses offer insights for advocating a voice for the Bunya tree whilst safeguarding its cultural and ecological significance through education, advocacy, and agency. This article presents five insights gleaned from our collective responses. These are 1. honour traditional knowledge and custodianship; 2. build collaborative networks and capacity to respond to ecological decline; 3. leverage art for ecological awareness and action. 4. empower community and business leadership; 5. catalyse awareness into action. These insights are offered not as definitive solutions but as a framework for thinking and acting that may support navigating the challenges of tree dieback and regenerative forest practices.

This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme X of prime characteristic. The main result is that when the Frobenius map on X is finite, for any compact generator G of $\mathsf {D}(X)$ the Frobenius pushforward $F ^e_*G$ generates the bounded derived category whenever $p^e$ is larger than the codepth of X, an invariant that is a measure of the singularity of X. The conclusion holds for all positive integers e when X is locally complete intersection. The question of when one can take $G=\mathcal {O}_X$ is also investigated. For smooth projective complete intersections it reduces to a question of generation of the Kuznetsov component.

In March 2020, nine EU heads of state co-signed a letter demanding a coordinated response to the pandemic and the adoption of common debt. Recent literature has shown the relevance of the European Council in the response to the pandemic, as well as the rising importance of interstate coalitions in EU policymaking. Yet, empirical understanding of these coalitions is limited, and the literature largely assumes their constitution along ‘structuralist’ logics (e.g., ‘debtors’ vs. ‘creditors’). The emergence of a ‘solidarity coalition’ proposing the ‘coronabond’ is puzzling for its contrast with the euro crisis. The aim of this paper is to explain how these countries coalesced and to understand how that relates and informs a shift in the imperatives of ‘responsible government’ in the EU. Tracing the negotiation of the letter, through interviews and discourse analysis, the paper makes a critical contribution to our understanding of the evolution in EU economic governance.

In this paper, we solve an exit probability game between two players, each of whom controls a linear diffusion process. One player controls its process to minimize the probability that the difference of the processes reaches a low level before it reaches a high level, while the other player aims to maximize the probability. By solving the Bellman–Isaacs equations, we find the sub-value and sup-value functions of the game in explicit forms, which are twice continuously differentiable. The optimal plays associated with the sub-value and sup-value are also found explicitly.

The study examined the effects of sociolinguistic background, nonverbal reasoning, and phonological working memory (WM) on heritage language (L1) and second language (L2) skills in Heritage Bilingual (HB) children attending preschool, considering relationships between L1 and L2 abilities. A total of 108 HB children completed vocabulary, morphosyntactic, nonverbal reasoning, and phonological WM tasks in both L1 and Italian (L2). Sociolinguistic background, including socio-economic status and linguistic history, was assessed through parental interviews. The analysis of reciprocal correlations between L1 and L2 showed within-language relationships and cross-language correlations only for morphosyntactic skills. Sociolinguistic background significantly influenced vocabulary skills, particularly in L1, while nonverbal reasoning impacted morphosyntactic skills, especially in L2. The findings highlight the importance of supporting families in enriching linguistic input in the heritage language and underscore the role of nonverbal reasoning and phonological WM in developing L2 competencies.

Ankle-foot mechanisms are designed to substitute for missing anatomical behavior of lower-limb prosthesis users. Historically, the majority of ankle-foot mechanism research has been focused on transtibial prosthesis users despite evidence that current knowledge is not directly translated to transfemoral prosthesis users, such as the influence of single-axis knee alignment during gait and the differences in standing balance management. This review attempts to characterize the current state of published knowledge about the effects of ankle-foot prosthesis design on standing and walking performance in transfemoral prosthesis users. The databases of PubMed, Embase, Cochrane Library, CINAHL, and IEEE Xplore were searched on January 6, 2025. Data from the selected articles were extracted and reported following the PRISMA extension for scoping reviews. Thirty-five articles were included that reported on seven different types of feet, ranging from simple designs like a solid ankle-cushioned heel (SACH) foot to more complex ones such as a microprocessor foot. The range of reported study tasks extended from standing and level walking to more complex tasks like incline/decline slopes and parcourse walking. The results suggest some parallels between transfemoral and transtibial prosthesis users, such as improvements with the incorporation of roll-over-shape (ROS) features and adaptation of a hydraulic ankle. The literature also emphasized how ankle-foot components affect ground force vector position and direction, influencing prosthetic knee control, highlighting the importance of considering the interaction between the prosthetic ankle-foot and knee mechanisms. Understanding these interactions will support the development of clinical practice guidelines by identifying the pair of prosthetic components that maximizes performance.

We estimate key parameters for the Galactic globular clusters NGC 1904 (M79) and NGC 4372. Additionally, we update the parameters for NGC 288, NGC 362, NGC 5904 (M5), NGC 6205 (M13), and NGC 6218 (M12), which were analysed in our previous papers, to incorporate significant advancements in data sets and isochrones in recent years. We fit various colour–magnitude diagrams (CMDs) of the clusters using isochrones from the Dartmouth Stellar Evolution Database and the Bag of Stellar Tracks and Isochrones, adopting an $\alpha$–enrichment value of $[\alpha/\text{Fe}] = +0.4$. The CMDs are constructed from data sets provided by the Hubble Space Telescope, Gaia, SkyMapper Southern Sky Survey Data Release 4, a large compilation of ground-based observations by Stetson, and other sources, using multiple filters for each cluster. Our cross-identification of almost all the data sets with those from Gaia or Hubble Space Telescope allows us to use their astrometry to precisely select cluster members in all the data sets. We obtain the following estimates, along with their total uncertainties, for NGC 288, NGC 362, NGC 1904, NGC 4372, NGC 5904, NGC 6205, and NGC 6218, respectively: metallicities [Fe/H]$=-1.28\pm 0.08$, $-1.26\pm 0.07$, $-1.64\pm 0.09$, $-2.28\pm 0.09$, $-1.33\pm 0.10$, $-1.56\pm 0.09$, and $-1.27\pm 0.10$ dex; ages $12.94\pm 0.76$, $10.33\pm 0.75$, $13.16\pm 0.76$, $12.81\pm 0.81$, $11.53\pm 0.76$, $12.75\pm 0.76$, and $13.03\pm 0.81$ Gyr; distances $8.83\pm 0.21$, $9.00\pm 0.21$, $12.66\pm 0.36$, $5.17\pm 0.15$, $7.24\pm 0.16$, $7.39\pm 0.08$, and $4.92\pm 0.13$ kpc; reddenings $E(B-V)=0.022\pm 0.024$, $0.029\pm 0.025$, $0.031\pm 0.018$, $0.545\pm 0.032$, $0.045\pm 0.027$, $0.024\pm 0.021$, and $0.210\pm 0.028$ mag; extinctions $A_{V}=0.09\pm 0.06$, $0.09\pm 0.06$, $0.11\pm 0.06$, $1.58\pm 0.06$, $0.13\pm 0.06$, $0.09\pm 0.06$, and $0.67\pm 0.06$ mag; and extinction-to-reddening ratio $R_{V}=3.9\pm 0.7$, $3.0\pm 0.5$, $3.8\pm 0.5$, $2.9\pm 0.4$, $2.9\pm 0.2$, $3.6\pm 0.7$, and $3.2\pm 0.1$. The $R_{V}$ estimates are fairly accurate, as the cross-identification of data sets enables us to calculate extinction across all ultraviolet, optical, and infrared filters used, thereby allowing us to derive an empirical extinction law for each combination of cluster, data set, and model. We confirm that the differences in horizontal branch morphology among the 16 Galactic globular clusters analysed in our studies can be explained by variations in their metallicity, age, mass-loss efficiency, and the loss of low-mass members during cluster evolution. Accordingly, most clusters indicate a relatively high mass-loss efficiency, consistent with the Reimers mass-loss law with $\unicode{x03B7} \gt 0.3$.

The decentralized international legal order arguably creates structural incentives for states to utilize INTERPOL—an entity of virtually universal membership—to reduce gaps in transnational police cooperation. One of INTERPOL’s iconic actions is the release of a Red Notice. It is the publication of decentralized requests by a member country or approved international entities such as the International Criminal Court (ICC),1 asking police worldwide to locate and, if applicable domestic law and treaties permit, provisionally arrest wanted persons or restrict their movement, pending extradition or surrender.2 Although INTERPOL does not have legal authority to oblige members to arrest persons in question, a Red Notice regularly leads to border stops or arrest pending extradition, travel or visa denials, and knock-on effects such as banking and employment difficulties. The fragmented international legal order may have paradoxically generated structural incentives to support a level of centrality represented by INTERPOL.

In this paper, we study the quantitative recurrence properties in the case of $\mathbb {Z}$-extension of Axiom A flows on a Riemannian manifold. We study the asymptotic behavior of the first return time to a small neighborhood of the starting point. We establish results of almost everywhere convergence, and of convergence in distribution with respect to any probability measure absolutely continuous with respect to the infinite invariant measure. In particular, our results apply to geodesic flows on the $\mathbb {Z}$-cover of compact smooth surfaces of negative curvature.