We explore the injectivity of the evaluation map $\mathrm {eva}_{f,\mathcal {A}} : \mathcal {A}^m \to \mathcal {A} $, where $ \mathcal {A} $ is an associative algebra over a field $ F $ and $ f $ is a polynomial in $ m \geq 1 $ variables with coefficients in F. Our investigation reveals that injectivity is possible only when $ m = 1 $ and $ f $ has degree one; for functions in two or more variables, such injectivity is impossible.

The importance of the third sector has been recognized by academia and policymakers. However, little is known about the geography of third sector associations. This issue is of central importance as the third sector is increasingly expected to play a role in solving local societal challenges. Here, the geography of the third sector is investigated at the municipal level in Finland using quantitative data and statistical analyses. The results show that socio-economically less advantageous and rural regions host the most third sector associations per capita. This creates a conundrum. On the one hand, there are abundant numbers of third sector associations in rural regions that could step in to address local societal challenges. On the other hand, rural regions are among the most poorly locally resourced, casting doubt on the future of their operations.

There is growing emphasis on the importance of active partner engagement in research and the design, planning, and implementation of new programs. Indeed, the science of engagement is gaining is receiving more attention from researchers, being formally included in research studies more often, and increasingly being required by funders. Financial costs and economic implications are well-known drivers of successful adoption, implementation, and sustainment of evidence-based programs; however, partner engagement costs are often excluded from economic evaluations even when elements of engagement may be relevant to sustainment and replication. Resource constraints in both research and practice highlight the need to better understand engagement costs to ensure that scarce resources are put towards the richest engagement activities. As part of the Rapid and Rigorous Patient-Centered Program (R2P2) in Colorado, we designed an approach to systematically document and analyze partner engagement costs across four prototype projects. We describe this approach, summarize needed adaptations, share an interactive data collection template, synthesize the relevant engagement costs during implementation, replication, and sustainment, and discuss lessons learned. Our experiences in R2P2 in costing initial engagement activities across four diverse projects offer direction for future research and practice that balances high-quality partner engagement with efficiency in addressing resource constraints facing researchers and practitioners.

There are long-standing debates on the social organisation and interactions of the first farmers of west-central Europe (the Linear Pottery culture/LBK, c. 5500–5000 BCE). Here we focus on a specific type of ceramic ware, Limburg pottery, whose morpho-stylistic features and bone temper stand in stark contrast to typical LBK pottery. Despite this, most Limburg vessels are found in LBK settlements. Researchers have proposed a variety of interpretations, ranging from pottery made by hunter-gatherers, to special-purpose vessels made by early farmers. This article provides a high-resolution reconstruction of the production sequences, using Limburg pottery from the Aisne Valley (Picardy, France), to address the identity of its producers, their learning networks and distribution channels, and the social practices associated with these artefacts. While Limburg pottery from the Aisne Valley forms a coherent stylistic group, it comprises two technical traditions, with one group of producers only making Limburg vessels, and the other usually making LBK vessels but occasionally producing Limburg vessels. Both groups display similar patterns of use, including dairy processing. Limburg vessels were therefore not marginal in LBK contexts, but functionally embedded in food practices rooted in farming lifeways. We hence propose a new model for interpreting the emergence and development of Limburg pottery, emphasising its role as ‘boundary objects’ within LBK communities and with communities outside of the LBK area. Ultimately, this socio-cognitive approach to pottery offers a deeper understanding of the social processes that shaped the cultural landscape of western Europe in the second half of the 6th millennium.

Hogg and Bushell’s “The Charter Dialogue between Courts and Legislatures” sparked a debate concerning the extent to which legislatures respond to the Supreme Court of Canada’s decisions in which the judges invalidate laws under the Charter of Rights and Freedoms. After constructing and coding a dataset of all relevant Charter cases between 2010 and 2023, this paper finds that the legislatures complied with rulings made by the Court in 93.3 per cent (or 28 out of 30) of the cases. It nevertheless demonstrates how the two non-compliant replies (to Bedford on sex work and to Carter on medical assistance in dying) are exceptional in that they featured strong interest-group support for upholding the constitutionality of the challenged provisions and thus straying from the Court’s rulings that invalidated them. This paper argues that while legislatures overwhelmingly comply with Charter rulings, interest-group support may help explain rare instances of legislative noncompliance.

Charismatic renewal and radical Christianity were movements of the ‘long’ 1960s. They both saw themselves as ‘new Reformations’ but have seldom been examined together. This article claims that ‘renewed’ and ‘religionless’ Christianity were more related than usually assumed. Both responded to a profound sense of religion-in-crisis. They were deeply eschatological and in different ways emphasised the Spirit. Despite some obvious dissimilarities, they were opposite sides of the same coin. Furthermore, they were entangled in unexpected ways. This points towards deeper undercurrents of religious thought and experience at work during the period and invites a wider appreciation of the significance of both eschatology and pneumatology in the Churches during the Sixties.

Recently a new type of generative artificial intelligence, agentic artificial intelligence, has been developed that extends product capabilities to act autonomously. Although agentic artificial intelligence systems offer a unique approach to supporting physicians, the products also pose many validity, privacy and security risks. Physicians need to understand the basic features of agentic artificial intelligence.

Mental healthcare respecting human rights is a worldwide need, yet research into practices that support such rights is limited. The United Nations Convention on the Rights of Persons with Disabilities, 2006 and the United Nations Resolution on mental health and psychosocial support, 2023 each heighten the urgency and the legal, as well as moral, social, political and other obligations to improve the quality of mental healthcare and respect human rights worldwide. It is useful to be specific about the actions to be taken, as done in recent programmes by the World Psychiatric Association and the World Health Organization. The work requires partnerships at all levels, from global to local, among healthcare professionals, people with lived experience and their families, communities and policy-makers. We present a themed series of papers developed in two parts: one related to principles of human rights-based mental healthcare; the other to assessment, policy and actions needed for tackling the implementation gap.

Neurosymbolic AI combines neural networks with symbolic programs to create robust and explainable predictions. One such framework is NeurASP, which trains a neural network to predict concepts and reasons over them using rules written in answer set programming (ASP) to solve downstream tasks. Crucially, labels are only provided for the downstream prediction produced by the symbolic rules, not for the latent concepts themselves. Backpropagation through the non-differentiable ASP component requires expensive probability and gradient calculations, which has hindered scalability to more sophisticated tasks. In this paper, we address the current limitations of NeurASP by improving its computational performance through vectorization, batch processing, and caching of intermediate computations during training. We compare computation speeds between the original and our new implementation of NeurASP and report speedups of multiple orders of magnitude for larger tasks. To this end, we propose a new dataset of difficult tasks involving playing cards, which we use to test the capabilities of NeurASP’s enhanced learning function.

This paper outlines a prospective cognitive framework for understanding the intersectionality of gender diversity and neurodivergence (specifically being autistic). The framework aims to provide understanding of the overlap between being autistic and being transgender and gender diverse, where these two constructs intersect and where they are disparate. Within these two intersections, there is evidence that individuals may mask or camouflage parts of these intersections of their identity, which may in turn impact on emotional wellbeing. This framework aims to be supportive of staff and adult service users alike in understanding this intersectionality and to provide suggestions on how to use this framework within psychological therapy to support autistic transgender and gender diverse adults. Limitations, clinical implications and key messages are briefly included within the discussion. Due to the limited research in this area at present, it is likely that further research into this field is warranted and further evidence, service user feedback and trialling of the cognitive framework would be imperative to conclude its utility and efficacy in clinical practice.

The integration of large language models (LLMs) into KUKA industrial robots offers a promising pathway toward intuitive natural language control and a higher level of intelligence. However, existing methods face two primary challenges: their reliance on predefined motion primitives and the syntactic fragility imposed by the strict constraints of proprietary KUKA Robot Language (KRL). To address these challenges, we propose MIKI (multi-agent integrated KUKA interface), a decoupled dual-agent framework that bridges high-level reasoning and low-level syntactic verification for industrial robot programming. The controller agent incorporates a chain-of-thought (CoT) reasoning mechanism to systematically decompose abstract human instructions into logical intermediate steps. By leveraging a visual toolchain, it translates these reasoned plans into a sequence of executable actions, each embedded with precise world coordinates. Subsequently, the code generation agent employs a syntax-guided iterative refinement process, underpinned by an ANTLR4 parser, to transform these actions into verified and executable KRL code. Experimental results demonstrate that this closed-loop approach substantially improves the syntactic success rate of code generation from 0.61 to 0.89. Furthermore, the framework achieves an average success rate of 0.6 across five desktop manipulation tasks of varying complexity using a physical KUKA robotic arm, validating its effectiveness in bridging high-level cognitive reasoning with deterministic industrial execution.

The article analyzes ethno-demographic trends in the contemporary Russian Federation, first of all, from the point of view of the probability of the development of separatist aspirations in ethnic autonomies within it. In recent decades, due to the shrinking opportunities to maintain the identity of indigenous peoples, assimilation processes have intensified among many of them (primarily the peoples of the Finno-Ugric group, as well as peoples whose is subjected to persecution in Russia, such as Ukrainians). Because of the assimilation, the share of the Russian ethnic majority in the country’s population is growing. At the same time, in the national republics of the North Caucasus and Siberia, the number of indigenous peoples is growing. In general, there is a process of ethnic separation: “Russian” regions are becoming ethnically more and more “Russian,” while 13 out of 21 republics are getting more and more “non-Russian.” Russian aggression in Ukraine also increases the likelihood of destabilizing Russia in the future, as the ideology of the “Russian World” politicizes inter-ethnic relations within Russia itself, making ethnic minorities second-class citizens.

Wind energy stands out as a promising clean and renewable energy alternative, not only for its potential to combat global warming but also for its capacity to meet the ever-growing demand for energy. However, analysis of wind data to fully harness the benefits of wind energy demands tackling several related challenges: (1) Current data resolution is inadequate for capturing the detailed information needed across diverse climatic conditions; (2) Efficient management and storage of real-time measurements are currently lacking; (3) Extrapolating wind data across spatial specifications enables analysis at costly-to-measure, unobserved points is necessary. In response to these challenges, we introduce the One Stone Three Bird model, a modality-agnostic learning framework utilizing Implicit Neural Network. Our model effectively compresses a large volume of climate data into a manageable latent codec. It also learns underlying continuous climate patterns, enabling reconstruction at any scale and supporting modality transfer and fusion. Extensive experimental results show consistent performance improvements over existing baselines in both (1) continuous super-resolution reconstruction and (2) data compression tasks for different cross-altitude prediction scenarios. Through systematic ablation studies, we demonstrate the effectiveness of each core component, quantifying its individual contribution to the overall performance of the proposed design.