This paper extends the overview (Mitchell et al. [11]) relating graphic statics and reciprocal diagrams to linear algebra-based matrix structural analysis. Focus is placed on infinitesimal mechanisms, both in-plane (linkage) and out-of-plane (polyhedral Airy stress functions). Each self-stress in the original diagram corresponds to an out-of-plane polyhedral mechanism. Decomposition into sub-polyhedra leads to a basis set of reciprocal figures which may then be linearly combined. This leads to an intuitively-appealing approach to the identification of states of self-stress for use in structural design, and to a natural "structural algebra" for use in structural optimisation. A 90° rotation of the sub-reciprocal generated by any sub-polyhedron leads to the displacement diagram of an in-plane mechanism. Any self-stress in the original thus corresponds to an in-plane mechanism of the reciprocal, summarised by the equation s = M* (where s is the number of states of self-stress in one figure, and M* is the number of in-plane mechanisms, including rigid body rotation, in the other). Since states of self-stress correspond to out-of-plane polyhedral mechanisms, this leads to a form of "conservation of mechanisms" under reciprocity. It is also shown how external forces may be treated via a triple-layer Airy stress function, consisting of a structural layer, a load layer, and a layer formed by coordinate vectors of the structural perimeter.

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IntroductionHealth benefits of regular participation in physical activity are well documented but population levels are low. Office layout, and in particular the number and location of office building destinations (eg, print and meeting rooms), may influence both walking time and characteristics of sitting time. No research to date has focused on the role that the layout of the indoor office environment plays in facilitating or inhibiting step counts and characteristics of sitting time. The primary aim of this study was to investigate associations between office layout and physical activity, as well as sitting time using objective measures.Methods and analysisActive buildings is a unique collaboration between public health, built environment and computer science researchers. The study involves objective monitoring complemented by a larger questionnaire arm. UK office buildings will be selected based on a variety of features, including office floor area and number of occupants. Questionnaires will include items on standard demographics, well-being, physical activity behaviour and putative socioecological correlates of workplace physical activity. Based on survey responses, approximately 30 participants will be recruited from each building into the objective monitoring arm. Participants will wear accelerometers (to monitor physical activity and sitting inside and outside the office) and a novel tracking device will be placed in the office (to record participant location) for five consecutive days. Data will be analysed using regression analyses, as well as novel agent-based modelling techniques.Ethics and disseminationThe results of this study will be disseminated through peer-reviewed publications and scientific presentations. Ethical approval was obtained through the University College London Research Ethics Committee (Reference number 4400/001).

Little is known of the patterns of physical activity, standing and sitting by office workers. However, insight into these behaviours is of growing interest, notably in regard to public health priorities to reduce non-communicable disease risk factors associated with high levels of sitting time and low levels of physical activity. With the advent and increasing availability of indoor tracking systems it is now becoming possible to build detailed pictures of the usage of indoor spaces. This paper reports initial results of indoor tracking used in conjunction with the ActivPAL activity monitoring device. In this paper we give an overview of the usage of the tracking system and its installation and illustrate some of the resultant data. We also provide preliminary results that investigate the relationship between location, light physical activity and sitting in a small sample of office workers (n=33) from two separate office environments in order to demonstrate the relevance and explanatory power of the technique.

For over 20 years, the term ‘cosmic web’ has guided our understanding of the large-scale arrangement of matter in the cosmos, accurately evoking the concept of a network of galaxies linked by filaments. But the physical correspondence between the cosmic web and structural engineering or textile ‘spiderwebs’ is even deeper than previously known, and also extends to origami tessellations. Here, we explain that in a good structure-formation approximation known as the adhesion model, threads of the cosmic web form a spiderweb, i.e. can be strung up to be entirely in tension. The correspondence is exact if nodes sampling voids are included, and if structure is excluded within collapsed regions (walls, filaments and haloes), where dark-matter multistreaming and baryonic physics affect the structure. We also suggest how concepts arising from this link might be used to test cosmological models: for example, to test for large-scale anisotropy and rotational flows in the cosmos.