We prove the central limit theorem (CLT), the first-order Edgeworth expansion and a mixing local central limit theorem (MLCLT) for Birkhoff sums of a class of unbounded heavily oscillating observables over a family of full-branch piecewise $C^2$ expanding maps of the interval. As a corollary, we obtain the corresponding results for Boolean-type transformations on $\mathbb {R}$. The class of observables in the CLT and the MLCLT on $\mathbb {R}$ include the real part, the imaginary part and the absolute value of the Riemann zeta function. Thus obtained CLT and MLCLT for the Riemann zeta function are in the spirit of the results of Lifschitz & Weber [Sampling the Lindelöf hypothesis with the Cauchy random walk. Proc. Lond. Math. Soc. (3) 98 (2009), 241–270] and Steuding [Sampling the Lindelöf hypothesis with an ergodic transformation. RIMS Kôkyûroku Bessatsu B34 (2012), 361–381] who have proven the strong law of large numbers for sampling the Lindelöf hypothesis.

The Atlantic Forest is one of the most threatened tropical forests in the world. Many species have declined and become isolated because of pervasive forest loss and degradation. Here we assess the current population status of Atlantic Forest tree species from Santa Catarina state in southern Brazil to inform conservation policies and future management and protection. We used a novel methodology to generate automated conservation assessments from forest surveys and herbaria data, based on IUCN criteria A, B, C and D. We assessed more than 500 tree species whose populations are considered threatened. Population size reduction (i.e. IUCN criterion A) was the main indicator of threat, followed by restricted geographical range (criterion B). We observed population reductions of over 50% over three generations in more than 60% of the assessments. We recommend including taxonomically verified herbaria data to improve the accuracy of conservation assessments. The results obtained here can be used to identify important and potential regions for creating protected areas and implementing forest restoration programmes.

The ability to manage money is essential for independent functioning but highly sensitive to cognitive decline. Managing money involves more than deploying skills rationally; it is influenced by a range of emotional and psychosocial factors. There is relatively little knowledge about how older adults, families and care professionals working with older people navigate and experience potential challenges of declining mental capacity to manage money. This article draws on a UK-based study involving 13 older people and/or family members and 28 social sector professionals, and their experiences of supporting older people with cognitive decline to manage money, triangulated with public information resources from major national organisations across the health, care, consumer and charity sectors. It focuses on the emotive and personal nature of cognitive decline and money management. Declining mental capacity to manage money can strike at the core of people’s sense of who they are, leading to strong tensions and difficulties in discussing support. Support to manage money is often framed in discussions as ‘there if we need it’; this can be reassuring for people, but may be challenged if there are subsequent disagreements and changes in perspectives about the detail and timing of support. These nuances are not well reflected in public information resources, which largely emphasise administrative procedure. Financial organisations may lack empathy that declining mental capacity to manage money is extremely challenging. The article highlights a greater need for recognition of the emotional and psychosocial complexities presented by declining mental capacity to manage money in later life.

Within the broad context of design research, joint attention within co-creation represents a critical component, linking cognitive actors through dynamic interactions. This study introduces a novel approach employing deep learning algorithms to objectively quantify joint attention, offering a significant advancement over traditional subjective methods. We developed an optimized deep learning algorithm, YOLO-TP, to identify participants’ engagement in design workshops accurately. Our research methodology involved video recording of design workshops and subsequent analysis using the YOLO-TP algorithm to track and measure joint attention instances. Key findings demonstrate that the algorithm effectively quantifies joint attention with high reliability and correlates well with known measures of intersubjectivity and co-creation effectiveness. This approach not only provides a more objective measure of joint attention but also allows for the real-time analysis of collaborative interactions. The implications of this study are profound, suggesting that the integration of automated human activity recognition in co-creation can significantly enhance the understanding and facilitation of collaborative design processes, potentially leading to more effective design outcomes.

This article explores the formation of public perceptions and the evolving historical reputation of Eleftherios Venizelos, arguably the most prominent Greek statesman of the twentieth century. While Venizelos actively cultivated his legacy during his lifetime, the article argues that it was the interplay of posthumous socio-political developments, cross-partisan commemorations and deliberate memory work that gradually solidified his image as a national figure. Focusing on the period from his death in 1936 until the imposition of the military dictatorship in 1967, the article shows how the overlap between Greece’s two major twentieth-century divides – the National Schism and the Civil War – shaped the trajectories of his memory. Tracing these shifts across political uses, historiographical portrayals and public commemorations, the article also engages broader debates on charismatic leadership, political myth and the making of national heroic figures, situating the Greek case within a wider comparative framework.

Recent studies reveal the central role of chaotic advection in controlling pore-scale processes including solute mixing and dispersion, chemical reactions, and biological activity. These dynamics have been observed in porous media (PM) with a continuous solid phase (such as porous networks) and PM comprising discrete elements (such as granular matter). However, a unified theory of chaotic advection across these continuous and discrete classes of PM is lacking. Key outstanding questions include: (i) topological unification of discrete and continuous PM; (ii) the impact of the non-smooth geometry of discrete PM; (iii) how exponential stretching arises at contact points in discrete PM; (iv) how fluid folding arises in continuous PM; (v) the impact of discontinuous mixing in continuous PM; and (vi) generalised models for the Lyapunov exponent in both PM classes. We address these questions via a unified theory of pore-scale chaotic advection. We show that fluid stretching and folding (SF) in discrete and continuous PM arise via the topological complexity of the medium. Mixing in continuous PM manifests as discontinuous mixing through a combination of SF and cutting and shuffling (CS) actions, but the rate of mixing is governed by SF only. Conversely, discrete PM involves SF motions only. These mechanisms are unified by showing that continuous PM is analogous to discrete PM with smooth, finite contacts. This unified theory provides insights into the pore-scale chaotic advection across a broad class of porous materials and points to design of novel porous architectures with tuneable mixing and transport properties.

In a close replication study of Darcy et al., (2016), Huensch (2024) reported a lack of clear relationships between inhibitory control (IC) and phonological processing, contrary to the initial findings. Given the general unreliability of response-time differences, which are often the basis of IC measures and could potentially mask small effects, we performed secondary analyses on Huensch’s (2024) open data set to investigate (a) the extent to which the reliability of IC measures could be improved using model-based approaches (Hui & Wu, 2024), (b) the correlations between the different IC tasks, and (c) their predictive power for phonological processing, based on the more reliable indices. Results showed that model-based approaches generally improved reliability, and particularly for the Stroop and Simon tasks to acceptable levels. Yet, correlations between IC tasks remained low, and partial correlation and hierarchical regression still failed to reveal significant relationships between IC and phonological processing, further confirming Huensch’s (2024) findings.

This introduction to the Agora outlines the issues raised by and arguments in Itamar Mann’s article, ‘From survival cannibalism to climate politics: Rethinking Regina vs Dudley and Stephens’, and the four commentaries thereon.

Richard Simon has long presented an enigma for historians, as his status as a pathbreaking textual critic and the opposition his work engendered from contemporary ecclesiastical authorities has sat uncomfortably alongside his consistent advocacy of his Catholic credentials. This article approaches this problem via an analysis of two hitherto understudied parts of his scholarly corpus. It first elucidates Simon’s distinctive plan for a new polyglot Bible in the mid-1680s before shifting attention some fifteen years to consider his work in French vernacular biblical translation, bringing out how the confessionally inflected content of his work in that field contrasted with his earlier critical scholarship. By revealing how Simon negotiated the relationship between scholarship and religion during his working life, the article foregrounds the continued import of confessionalized erudition at the turn of the eighteenth century while also interrogating the limits of its explanatory power as a historical category.

This study examines Taiwanese netizens’ metapragmatic debates on tonal variation in Taiwan Mandarin, focusing on the pronunciation of 企業 qìyè ‘company/enterprise’ by two government officials during a nationally broadcast press conference. It investigates how the non-standard variant qǐyè, a relic feature historically present in Taiwan, becomes enregistered as a linguistic emblem of imported Chinese influence through the processes of clasping and semiotic differentiation. The study highlights the ideological stakes in linguistic boundary-making and explores how tonal variation functions as a site for negotiating national identity. It further connects this linguistic debate to broader ideological projects such as democratization, Taiwanization, and shifting Taiwan-China relations. By integrating variationist and metapragmatic approaches, this study contributes to discussions on the indexical field and the role of explicit metapragmatic commentary in shaping linguistic change. (Indexicality, language ideology, tonal variation, enregisterment, language policing, metapragmatics, Taiwan)

In this paper, we describe finite order entire solutions of nonlinear partial differential equation

\begin{equation*} \prod _{i=1}^n\left (a_{i 1} u_{z_1}+a_{i 2} u_{z_2}+\cdots +a_{i n} u_{z_n}\right )=1 \end{equation*}

The commodity frontiers framework describes well the movement of sugar cultivation across the Mediterranean, Atlantic, and Caribbean. But it is less effective when explaining the evolution of sugar in nineteenth-century Tamil Nadu. In Tamil Nadu, the high costs of cultivation discouraged many peasants and landowners from planting sugar cane. As a consequence, despite British pressure to plant more cane, there was little increase in the crop before the twentieth century. In Tamil Nadu, sugar made from palmyra juice was a viable and popular substitute for cane sugar and this further discouraged the expansion of cane cultivation. The jaggery made from palm juice satisfied the demand for sweetener from most consumers in the region. From the mid-nineteenth century, palm jaggery was the raw material for making white sugar and distilling arrack in the sugar mills that were built in the region. Regional conditions shaped the development of sugar cultivation and manufacturing in Tamil Nadu. It is not a story of interaction between the local and the global as is found in the commodity frontiers framework. The region is a scale of activity that possesses great explanatory power, as the case of nineteenth-century South India shows.

The Caribbean islands represent some of the most biologically diverse places on Earth, but much of that diversity is now at risk due to human impact. Larger islands in the Caribbean host more native species, but small islands still hold together a significant portion of the regional biota. Although our knowledge of extinct and extirpated taxa continues to improve, there are hundreds of islands, each with their own unique faunal histories from where there is little information about their ancient diversity. Sombrero is a very small island (0.38 km2) located within the limits between the Greater and Lesser Antilles and is largely barren of vegetation and freshwater. The island was extensively mined for bird guano in the 1800s, which profoundly altered its topography and fauna. Here, we describe a collection of microvertebrates recovered in 1964 from Sombrero, which documents an unexpectedly high number of colonization events and high extinction rate for this territory. The late Quaternary deposits from the island contain remains of five types of lizards, a snake, a tortoise, and an anuran that colonized the island once it became aerially exposed in the early Pleistocene. The ability for such a small, remote island to have eight colonizing taxa in < 2.5 Ma, provides support for the role that island hopping played in regional biodiversity in the Cenozoic (e.g., GAARlandia), even across small, barren islands. Furthermore, these fossils further show that large scale defaunation also affected vertebrate communities on very small islands in the Caribbean.