We confirm a conjecture posed by Bergelson, Moreira, and Richter, and in particular show that for every probability-measure-preserving system $(X,\mathscr {B},\mu ,T)$, every $k\in \mathbb {N}$, every set $A\in \mathscr {B}$ with $\mu (A)>0$, and every tempered function f, $ \lim _{N\to \infty }({1}/{N}) \sum _{n=1}^N\mu (A\cap T^{-\lfloor {f(n)\rfloor }}A\cap T^{-\lfloor {f(n+1)\rfloor }}A\cap \cdots \cap T^{-\lfloor {f(n+k)\rfloor }}A)>0. $ This is achieved by establishing conditions on an increasing function $W:\mathbb {N}\rightarrow (0,\infty )$ such that if $(x_n)_{n\in \mathbb {N}}$ is a bounded sequence in a Banach space with $ \lim _{W(N)-W(M)\to \infty }({1}/({W(N)-W(M)})) \sum _{n=M}^N (W(n)-W(n-1))x_n =L $ then the limit of Cesàro averages of $(x_n)_{n\in \mathbb {N}}$, $\lim _{N\to \infty }({1}/{N})\sum _{n=1}^Nx_n$, is also equal to L. Furthermore, the methods we develop can be used to sharpen some of the combinatorial results obtained by Bergelson, Moreira, and Richter. For example, if E is a set of positive upper density, then for any $k\in \mathbb {N}$, any $\varepsilon>0$, and all sufficiently large $N\in \mathbb {N}$ there is an $a\in \mathbb {N}$ and an $n\in [N-N^{1/2+\varepsilon },N]$ such that $\{a,a+\lfloor n^{3/2} \rfloor ,a+\lfloor (n+1)^{3/2}\rfloor ,\ldots ,a +\lfloor (n+k)^{3/2}\rfloor \}\subseteq E.$

Two forms of existential proposition are identified, one favoured by analytical philosophers, one by Thomists. It is argued, against objections, that both forms were recognized and used by Thomas. A useful way of labelling this point is to speak of the distinction between esse ut verum and esse reale: being in the sense of the true, the analytical notion, on the one hand, and the Thomist notion of actual or real existence on the other. The former is best expressed by a second-level predicable, the latter by a first-level predicable. Both express a valid notion which is fittingly called ‘existential’, and both are, indeed, analogically connected in meaning.

This study examines the role of business in tax policymaking through the lens of business power, focusing on the 1950 Tax Revision in the Netherlands as a historical case. The revision policy process unfolded in the context of post-war economic reconstruction and industrialization and became a key site of contention between fiscal and economic policy objectives, in which business interests were strongly represented. Combining historical methodology and process tracing with theoretical perspectives of business power, the study identifies the mechanisms through which business-government interactions operated in the tax policy process. Corporate actors advocated for fiscal relief by exploiting intra-governmental differences and leveraging their structural economic importance and close connections to the government. Crucially, they constructed a narrative framing fiscal relief as a necessity for industrial development, thereby using the reconstruction context to advance their interests.

This Guest Editorial argues that symptoms, rather than syndromic diagnoses alone, function as the practical units of psychiatric care. To render implicit symptom-oriented reasoning explicit, symptom-oriented clinical psychiatry offers a structured framework for analysing symptom roles, guiding treatment priorities and sequence and reducing reactive polypharmacy while remaining fully compatible with established diagnostic systems.

Missing-model problems are a type of problem that arises when scientists are trying to gain access to initially inaccessible phenomena. This paper describes what missing-model problems are, and examines examples of them from seismology, optics, and the theory of gases. It is argued that the examination of missing-model problems will give us a better understanding of the challenges scientists face when attempting to gain access. Two themes for the further study of missing-model problems are laid out: justification and representation.

To accompany the publication of the special issue, ‘Population-Level Data Linkages in Worldwide Twin Registries’, an online, interactive tool titled ‘Twin Registries Worldwide’ has been developed to provide an overview of twin registries across the globe. The tool currently offers a searchable table view that allows users to explore twin registries by country, registry name, recruitment period, sample size, phenotypic domains, availability of biological samples, and linkage to administrative or health-related databases.

Novel tools have allowed researchers to intervene into circuits at the mesoscale. The results of these interventions are often explained by appeal to functions. How are functions ascribed to circuit parts experimentally? I identify two kinds of function ascription practices in circuit interventions. Analysis of these practices shows us that what makes function ascriptions challenging is a lack of interventive control and insufficient constraints on the class of candidate functions to discriminate in practice. One kind of function ascription practice—subtractive analysis—fares better at addressing these challenges.

As China pursues high-quality, innovation-driven growth, it faces rising economic policy uncertainty (EPU) fuelled by information gaps, changing policy priorities and geopolitical tensions. Yet how EPU shapes green technology innovation remains contested. Analysing panel data from A-share listed companies (2009–2019), this study reveals that EPU motivates enterprises to improve green innovation levels. Mechanism analysis shows that EPU increases R&D investment and strengthens environmental, social and governance (ESG) performance, especially among large and state-owned enterprises, while significantly reducing the effectiveness of environmental subsidies. These findings suggest EPU acts as a strategic catalyst, though patent growth may partly reflect strategic filing behaviour rather than substantive technological progress. Consequently, policy frameworks must provide predictable, long-term support. Governments should improve subsidy mechanisms and promote adaptive R&D strategies to utilize uncertainty as a driver for green transformation. While the 2009–2019 scope ensures data reliability, the results’ external validity should be considered alongside post-2020 macroeconomic and geopolitical shifts.

Annually resolved radiocarbon (14C) records from tree rings provide a high-resolution archive for investigating short-term atmospheric 14C variations driven by solar and cosmic activity, as well as terrestrial processes, including geomagnetic modulation, stratosphere–troposphere exchange, ocean–atmosphere interactions, and tree physiological traits. While extensive data are available for the Northern Hemisphere, comparable high-resolution records from the Southern Hemisphere are scarce, making it difficult to obtain robust 14C calibration for the south and to evaluate 14C distribution models. Here, within the framework of the CHASCA project, we present a new annually resolved 14C record from Fitzroya cupressoides, a long-lived conifer native to southern South America, spanning AD 970–1084 (RAL060), with samples collected in North Patagonia, Argentina. This is the first annually resolved radiocarbon series from South America and among the longest for the Southern Hemisphere.

The CHASCA series shows strong agreement with Northern Hemisphere datasets and with SHCal20 confirming the expected interhemispheric offset. It also captures the AD 993–994 solar particle event, with a statistically significant level (≈ 7 σ), though with reduced amplitude compared to the shorter decade-long records from New Zealand and Chile. This attenuation may reflect a combination of stratospheric–tropospheric dynamics, regional environmental conditions, and species-specific growth dynamics, although these mechanisms remain speculative and require further investigation, underscoring the complexity of local expression of cosmogenic 14C signals. The CHASCA series thus extends the geographic coverage of annually resolved-14C datasets and establishes South America as a key region for detecting and comparing short-term cosmogenic events.

The extreme warmth of Marine Isotope Stage (MIS) 11 has been extensively studied in the terrestrial realm; however, less is known about its expression in the North Pacific. Here, we present a multiproxy record from Integrated Ocean Drilling Program (IODP) Site U1339 in the southeastern Bering Sea (Umnak Plateau). We use sedimentology, diatoms, and organic geochemistry to reconstruct sea ice and primary productivity from the end of MIS 12 to the beginning of MIS 10 (430–368 ka) at this site. In late MIS 12, the Umnak Plateau experienced extensive seasonal sea ice cover, with spring sea ice concentration near 100%. Based on diatoms and ice-rafted debris, sea ice declined to year-round ice-free conditions during deglaciation but readvanced during the interglacial climatic optimum. In contrast, sea ice has not been present at the Umnak Plateau throughout the Holocene. During MIS 11, sea ice at this site may have persisted due to a more easterly and/or weaker Aleutian Low. Laminated sediments indicate enhanced seasonal productivity during deglaciation. However, productivity does not remain high throughout the interglacial. The decline in productivity during MIS 11 occurs independently of fluctuations in sea ice and upwelling and may be due to increasing nutrient limitation.

We study the geometry of the complex hyperbolic triangle group $\Delta_{4,\infty,\infty;\infty}$ acting on the complex hyperbolic plane $\mathbf{H}^2_{\mathbb C}$ and show that the 3-manifold at infinity of $\Delta_{4,\infty,\infty;\infty}$ is the complement of the chain link $8^4_1$ in the 3-sphere. In particular, the four-cusped hyperbolic 3-manifold $S^3-8^4_1$ admits a spherical CR-uniformisation. Since the ideal boundary of the Ford domain is an infinite-genus handlebody, we introduce a new technique to construct embedded topological disks that cap off the genus, ensuring their boundaries are compatible with the side-pairings. This surgical approach facilitates the determination of the fundamental group of the manifold at infinity and simplifies the computation compared to [14].

Based on this result and previous studies, we conjecture that the chain link $C_p$ serves as an ancestor of the 3-manifold at infinity for the critical complex hyperbolic triangle group $\Delta_{p,q,r;\infty}$, where $3 \leq p \leq 9$.

We construct one of the longest continuous rent series for the pre-modern world, tracing Toledo’s housing market from 1489 to 1810. Using the Cathedral’s portfolio, we merge a hedonic microdataset (1489–1650) with a decadal census of leases (1650–1810), yielding over 34,000 transactions and coverage of up to 35% of dwellings in the city per sampled year. Privileged groups drove a bubble-like surge in rents during the sixteenth-century silver boom, while the working poor saw only modest increases. After 1600, the premiums once paid by artisans and shopkeepers over unskilled laborers steadily disappeared, marking the erosion of Toledo’s middle class. These findings underscore the role of housing markets in both reflecting and reinforcing inequality in early modern Spain.

Current geometric-based path-planning methods for vertical parking in automated parking systems face issues such as stringent initial position requirements, insufficient clearance from garage boundaries, and discontinuous curvature. To address these problems, this paper proposes a parking path-planning method that integrates the Reeds–Shepp curve with an improved particle swarm optimization (PSO) algorithm. The parking process is decomposed into forward and backward segments, each generated using the Reeds–Shepp curve to enhance flexibility. The shift point, defined as the transition between the two segments, serves as the decision variable in the PSO framework. The fitness function jointly considers path length and deviation between the target pose and garage entry. A quadratic Bézier curve and a nonlinear adaptation mechanism are incorporated into the PSO to determine the optimal shift point, mitigating the risk of proximity to garage boundaries. The initial path is then generated using the Reeds–Shepp curve based on the initial pose, shift point, and target pose. After discretization, the path points are optimized via a nonlinear optimization formulation to eliminate curvature discontinuities at segment junctions. Experimental results demonstrate that the proposed method generates feasible, continuous-curvature parking paths across a variety of initial poses, outperforming conventional approaches in terms of flexibility and clearance.