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Manufacturing industry is becoming more and more moving from linearity to circularity. There are several circular strategies to follow in their search to become more resource efficient and circular e.g. through remanufacturing. The aim of this paper is to describe the differences between remanufacturing definitions and how to redefine remanufacturing from an industrial perspective. To meet this aim, a literature study has been performed in academic and grey literature. A specific focus has given to definitions made in standards and legal documents since they have a strong impact on manufacturing industry. In addition, semi-structured interviews have been performed with industrial participants to get their view on this topic. Results show that there is a bit of confusion about how to define remanufacturing, mainly in the standardization community. This research recommends and new definition of remanufacturing according to industrial preferences.

PurposeIn a context where the transition to a circular economy is increasingly required, it is necessary to clarify the relationship between sustainability and circularity. In this commentary we summarise what are circularity indicators and what is LCA (Life Cycle Assessment), and we discuss their potential role in improving circular decision making.MethodsBased on literature, a focus on how circularity indicators and LCA could be used in circular decision making is presented. Moreover, an analysis of recent studies has been carried out to identify the relationship between LCA and circularity indicators.Results and discussionWe can state that no authors have concluded that circularity indicators can be used alone to choose the best option in circular economy projects. This is because the circularity indicators only provide a partial view on the environmental performance of a system. At the same time, it appears that the circularity indicators are easier to communicate, and a high degree of circularity could help to build good relationships with customers and increase reputation among stakeholders, as well as to have an easier access to funding.Conclusions and recommendationsAt the end, we propose a procedure to include both the LCA and the circularity measurement in the assessment of circular economy strategies. While still at an early stage of conceptualisation, it gives an idea on how to integrate environmental sustainability aspects into circular economy initiatives.

BackgroundOwing to the large amounts of energy, greenhouse gases, and waste that it generates, the construction industry is fundamental to the transition towards a circular economy. Indicators which show the circularity of products—and thus make them comparable with each other—can be used to support the implementation of such an economy. In this article, we have adapted the material circularity indicator of the Ellen MacArthur Foundation in order to analyze the circularity of construction products available in the German environmental database ÖKOBAUDAT.ResultsThe adapted indicator is applied to 89 building products from the categories of insulation materials, plastics, metals, and mineral building materials. More than half of the products receive the lowest score of 0.10, indicating poor implementation of circular strategies in the German construction industry to date.ConclusionCircular material flows are most likely to be employed for metals. However, the overall low circularity scores indicate a big need for better implementing circularity strategies.

Circular Economy (CE) has proved its contribution to addressing environmental impacts in the Architecture, Engineering, and Construction (AEC) industries. Building Circularity (BC) assessment methods have been developed to measure the circularity of building projects. However, there still exists ambiguity and inconsistency in these methods. Based on the reviewed literature, this study proposes a new framework for BC assessment, including a material flow model, a Material Passport (MP), and a BC calculation method. The material flow model redefines the concept of BC assessment, containing three circularity cycles and five indicators. The BC MP defines the data needed for the assessment, and the BC calculation method provides the equations for building circularity scoring. The proposed framework offers a comprehensive basis to support a coherent and consistent implementation of CE in the AEC industry.

Spatially explicit capture–recapture (SECR) models have emerged as one solution to the problem of estimating the population density of mobile and cryptic animals. Spatial models embody assumptions regarding the spatial distribution of individuals and the spatial detection process. The detection process is modeled in SECR as a radial decline in detection probability with distance from the activity center of each individual. This would seem to require that home ranges are circular. The robustness of SECR when home ranges are not circular has been the subject of conflicting statements. Ivan et al. previously compared the SECR density estimator to a telemetry-scaled non-spatial estimator. I suggest that the apparent non-robustness of SECR in their study was a simulation artefact. New simulations of elliptical home ranges establish that the SECR density estimator is largely robust to non-circularity when detectors are spread in two dimensions, but may be very biased if the detector array is linear and home ranges align with the array. Transformation to isotropy reduces bias from designs of intermediate dimension, such as hollow square arrays. Possible alignment of home ranges should be considered when designing detector arrays.

Arithmetic and logic seem to enjoy an especially close relationship. Frege once wrote that arithmetic is reason’s nearest kin. To deny any of the basic laws of arithmetic seems tantamount to denying a basic law of logic. My dissertation is concerned with two great attempts to make something more of this informal idea. In one direction, Frege tried to reduce arithmetic to nothing but quantificational logic and definitions. Neologicists continue to follow in Frege’s footsteps, pursuing a version of this program today. In the other direction, Gödel tried to reduce certain applications of quantificational logic to nothing but arithmetic and definitions, by means of his Dialectica translation. In the first half of my dissertation, I prove new theorems (with Jeremy Avigad) that shed a surprising light on the prospects for neologicism. An important objection against neologicism is that it makes use of allegedly stipulative definitions that are not conservative over pure logic, i.e., definitions that yield new consequences expressible in old vocabulary. This violates a basic requirement on stipulative definitions. I argue that by passing to a richer logical and definitional framework, it is possible to overcome the conservativeness objection. However, there is a subtlety: the strategy succeeds only if conservativeness is understood semantically rather than deductively. This suggests that the viability of neologicism is highly sensitive to the way in which epistemic commitments are represented in formal theories. In the second half of my dissertation, I argue that Gödel’s Dialectica translation succeeds in assigning a constructive meaning to quantificational theories of arithmetic. Virtually all commentators have objected that Gödel’s translation makes use of definitions which presuppose the very quantificational logic that Gödel was trying to eliminate. This would render the translation philosophically circular. Gödel was adamant that there was no circularity here. He attempted to explain the matter in a page-long footnote, which, however, no one has been able to understand. I vindicate Gödel, showing that there is no circularity and answering a longstanding exegetical question in Gödel scholarship. Abstract prepared by Stephen Mackereth E-mail: sgmackereth@gmail.com URL: http://d-scholarship.pitt.edu/id/eprint/46578

The manufacturing industry is undergoing a major transformation driven by the need to adopt sustainable and circular practices in product realisation. To manage and evaluate complex transitions, many sectors use maturity models—structured instruments that assess current capabilities and track progress. However, existing instruments rarely integrate both product and production development perspectives. This paper presents the development and application of a holistic maturity instrument tailored to product realisation in manufacturing. We outline its conceptual foundation, assessment criteria, and implementation methodology, and report initial findings from applications across ten manufacturing companies. Results indicate that the integration of sustainability and circularity in product realisation is generally fair, with variation across companies and aspects. Not too surprisingly, perceived knowledge of sustainability was higher than that of circularity among the participating companies. A challenging area appears to be data and information related to sustainability and circularity. Overall, satisfaction with the level of integration of sustainability and circularity aspects in product realisation among the participating companies was mainly neutral, neither dissatisfied nor satisfied. Beyond assessing maturity levels, the instrument fosters reflection and engagement, supporting the complex transition. We argue that the instrument has potential as a boundary object, facilitating dialogue, shared understanding, and collaboration across organisational functions and stakeholders.

The extension of sample entropy methodologies to multivariate signals has received considerable attention, with traditional univariate entropy methods, such as sample entropy (SampEn) and fuzzy entropy (FuzzyEn), introduced to measure the complexity of chaotic systems in terms of irregularity and randomness. The corresponding multivariate methods, multivariate multiscale sample entropy (MMSE) and multivariate multiscale fuzzy entropy (MMFE), were developed to explore the structural richness within signals at high scales. However, the requirement of high scale limits the selection of embedding dimension and thus, the performance is unavoidably restricted by the trade-off between the data size and the required high scale. More importantly, the scale of interest in different situations is varying, yet little is known about the optimal setting of the scale range in MMSE and MMFE. To this end, we extend the univariate cosine similarity entropy (CSE) method to the multivariate case, and show that the resulting multivariate multiscale cosine similarity entropy (MMCSE) is capable of quantifying structural complexity through the degree of self-correlation within signals. The proposed approach relaxes the prohibitive constraints between the embedding dimension and data length, and aims to quantify the structural complexity based on the degree of self-correlation at low scales. The proposed MMCSE is applied to the examination of the complex and quaternion circularity properties of signals with varying correlation behaviors, and simulations show the MMCSE outperforming the standard methods, MMSE and MMFE.

The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main advantage of this uniform approach is that the two proving techniques can be easily combined during the verification process. Circular induction is simple, flexible, generic, and therefore it is a good candidate framework for combining different proving schemes into a competitive tool. We exhibit this potential by presenting how the circular induction is implemented in CIRC, a prover built around the Circularity Principle. Disclaimer. This paper was written in 2010, at the time the CIRC prover was developed, and the main body reflects the state of the work and of the prover as of that date. For this arXiv technical report, only the related-work discussion (Section 6) and the concluding section have been revised: Section 6 has been extended to situate circular induction within the cyclic-proof and infinite-descent literature that has appeared or matured since 2010. No other part of the paper-its definitions, results, proofs, examples, or implementation description-has been modified, and the technical content should be read as a 2010 contribution. References to developments after 2010 appear only in the updated related-work section.

The circular economy (CE) in construction literature engages with individual CE concepts, mostly at the ‘macro’/‘meso’ levels, and lacks holistic frameworks of indicators for circularity assessments (CAs) to inform decision-making at the ‘micro’ (project) level. This article presents a model using the Analytic Hierarchy Process (AHP) for circular proposal selection in building projects based on a previously validated conceptual framework. The model involves twelve circularity indicators (CIs) classed under five themes relevant to building lifecycle stages. A questionnaire survey was used to establish the final weight vector of CIs. Participants acknowledged the immediate and prolonged effects of design on circularity and viewed waste as ‘design flaws’ but focused on aspirational design indicators relevant to achieving future circularity and missed opportunities for embedding circular materials in design. Moreover, UK participants showed distinctive behaviours towards CAs (proactive/reactive) based on work experience. ‘UK-Experts’ focused on ‘front-end’ design indicators, while ‘UK-Non-experts’ focused on ‘back-end’ waste management indicators. The findings indicate a partial transition to CE better described as a ‘recycle/reuse economy’. CAs and multiple-criteria decision-making (MCDM) techniques facilitate automated decision-making, which provides a new pathway to digital transformation within built environment. Future research will develop a decision-making tool and apply the proposed model in real-life projects.