Challenges related to the teaching and learning of formal notation in school mathematics are widely documented, and specifically in relation to the underlying mathematical structures that the notation is intended to convey. In this article, we draw on embodied cognition to examine the interactions among three students working with the software Grid Algebra. Embodied cognition emphasises the role of gesture and movement in learning and understanding mathematics. Grid Algebra uses movement to direct students' attention to mathematical operations on numbers and numerical expressions within the grid and the structure of these operations, while the software takes care of the formal notation of the numerical expressions that describe these sequences of operations. We analyse how different modes of communication work together to scaffold students' fluency with operations and the formal notation representing these operations and the order in which they are performed. The dynamic between notation, speech, movement and position allows students to educate their interpretation of mathematical notation through the movements and positions that they are very familiar with.
Reconfigurable manufacturing requires robotic workcells that can adapt to changing products, processes, and equipment without extensive redesign or manual reprogramming. This paper presents the R3M framework, a ROS 2 driven integration architecture that connects model based manufacturing knowledge with execution level robotic control. Product, process, and equipment information is formalised through UML domain models and serialised in AutomationML(AML), enabling automated correspondence between assembly requirements, available skills, and executable recipes. The framework integrates automated programme generation, reinforcement learning based recipe optimisation, and a modular CAD informed six degree of freedom perception layer to support both technical and semantic interoperability across simulated and physical workcells. The approach is evaluated through Cube Kitting and Cylinder Stacking use cases implemented on distinct robotic platforms, including ABB and Universal Robots systems. Experimental results show high reliability, with environment launch performance reaching up to 99.93%, standard skill sequences achieving 100% execution success, and full use case trials exceeding 97% success in simulation and reaching 100% on physical hardware. These findings demonstrate that R3M provides a scalable foundation for adaptive robotic manufacturing, reducing programming effort while supporting modular substitution, robust perception, and simulation to real deployment.
The circular economy (CE) is increasingly emphasised in 3D concrete printing (3DCP), yet evidence remains limited on the key barriers to its implementation and the enablers needed to support practical uptake. This study addresses that gap through a sequential mixed-methods design combining a literature-informed review to identify initial barriers, ten semi-structured expert interviews to refine them and elicit corresponding enablers in the 3DCP context, and a questionnaire survey of 58 academic and industry specialists from multiple regions to prioritise their relative importance using a fuzzy synthetic evaluation approach. The findings show that CE implementation in 3DCP is constrained less by isolated technical limitations than by wider system conditions shaping approval, investment, knowledge translation, and supply-chain coordination. Regulatory and standardisation issues emerged as the most critical barrier theme, followed by financial and market constraints, while the gap between low-TRL academic research and high-TRL industrial implementation was identified as the most prominent item-level barrier. The most influential enablers were CE-oriented standards, cost-effective process maturation, targeted R&D support, and stronger validation and implementation pathways. By revealing convergence between academia and industry on the main priorities, the study contributes a context-specific methodological approach for investigating CE implementation in 3DCP and establishes a prioritised evidence base on the barriers and enablers shaping circular 3DCP. It also provides practical guidance for researchers, industry stakeholders, and policy actors by identifying where intervention is likely to be most effective, particularly in standards development, technology validation, investment support, and supply-chain coordination, to scale circular 3DCP in support of net-zero and zero-waste ambitions.
Z2 symmetry is ubiquitous in quantum mechanics, where it drives various phase transitions and emergent physics. The role of Z2 symmetry in the thermalization of a local observable in a disordered system can be understood using random matrix theory. To do so, we consider random symmetric centrosymmetric (SC) matrix as a toy model where a Z2 symmetry, namely, the exchange symmetry, is conserved. Such a conservation law splits the Hilbert space into decoupled subspaces such that the energy spectrum of an SC matrix is a superposition of two pure spectra. After discussing the known results on the correlations of such mixed spectra, we consider different initial states and analytically compute the time evolution of their survival probability and associated timescales. We show that there exist certain low-energy initial states which do not decay over a very long timescales such that a measure zero fraction of random SC matrices exhibit spontaneous symmetry breaking. Later, we look at the equilibrium values of local observables like the density-density correlation, kinetic energy operator, and compare them against the average values from the microcanonical and canonical ensembles. We find that when the observable violates (respects) the global symmetry of the Hamiltonian, the equilibrium value is independent (dependent) of the symmetry of the initial state. However, irrespective of such symmetry constraints, the fluctuations of the diagonal terms of the observables within microcanonical shells decay with system size such that the ansatz of the eigenstate thermalization hypothesis remains valid. We show that the equilibrium value converges to the canonical average for all the observables and initial states, indicating that thermalization occurs despite the presence of a global symmetry.
This paper investigates the impact of rivals' Mergers and Acquisitions (M&A) activities on the innovation orientation of firms that are not directly involved in these transactions, hereafter referred to as focal firms. Drawing on the Awareness-Motivation-Capability (AMC) framework, we find that rivals' M&A activities positively affect a focal firm's exploratory innovation, while negatively influencing its exploitative innovation, a dynamic that is predominantly driven by rival firms acting as acquirers. We further identify key boundary conditions that moderate this relationship and find that the influence of rival acquirers is amplified when their M&A deals are exploitative in nature, suggesting that focal firms respond strategically by differentiating through exploration. In addition, high levels of market competition intensify the positive effect of rival acquirers on focal firms' exploratory innovation. Finally, focal firms with greater financial slack are more likely to shift their innovation orientation towards exploration in response to rivals' M&A. Together, our findings reveal how external strategic moves by rivals can trigger forward-looking innovation responses and highlight the importance of firm capabilities and market context in shaping these dynamics.
