Maxwell-Laman counts for bar-joint frameworks in normed spaces

The rigidity matrix is a fundamental tool for studying the infinitesimal rigidity properties of Euclidean bar-joint frameworks. In this paper we generalize this tool and introduce a rigidity matrix for bar-joint frameworks in arbitrary finite dimensional real normed vector spaces. Using this new matrix, we derive necessary Maxwell-Laman-type counting conditions for a well-positioned bar-joint framework in a real normed vector space to be infinitesimally rigid. Moreover, we derive symmetry-extended counting conditions for a bar-joint framework with a non-trivial symmetry group to be isostatic (i.e., minimally infinitesimally rigid). These conditions imply very simply stated restrictions on the number of those structural components that are fixed by the various symmetry operations of the framework. Finally, we offer some observations and conjectures regarding combinatorial characterisations of 2-dimensional symmetric, isostatic bar-joint frameworks where the unit ball is a quadrilateral.Comment: 17 page

Symmetric isostatic frameworks with ℓ1\ell^1 or ℓ∞\ell^\infty distance constraints

Combinatorial characterisations of minimal rigidity are obtained for symmetric 2-dimensional bar-joint frameworks with either $\ell^1$ or $\ell^\infty$ distance constraints. The characterisations are expressed in terms of symmetric tree packings and the number of edges fixed by the symmetry operations. The proof uses new Henneberg-type inductive construction schemes.Comment: 20 pages. Main theorem extended. Construction schemes refined. New titl

The digital code driven autonomous synthesis of ibuprofen automated in a 3D-printer-based robot

An automated synthesis robot was constructed by modifying an open source 3D printing platform. The resulting automated system was used to 3D print reaction vessels (reactionware) of differing internal volumes using polypropylene feedstock via a fused deposition modeling 3D printing approach and subsequently make use of these fabricated vessels to synthesize the nonsteroidal anti-inflammatory drug ibuprofen via a consecutive one-pot three-step approach. The synthesis of ibuprofen could be achieved on different scales simply by adjusting the parameters in the robot control software. The software for controlling the synthesis robot was written in the python programming language and hard-coded for the synthesis of ibuprofen by the method described, opening possibilities for the sharing of validated synthetic ‘programs’ which can run on similar low cost, user-constructed robotic platforms towards an ‘open-source’ regime in the area of chemical synthesis

The changing face of innovation policy: implications for the Northern Ireland economy

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Merging DNA metabarcoding and ecological network analysis to understand and build resilient terrestrial ecosystems

Summary 1. Significant advances in both mathematical and molecular approaches in ecology offer unprecedented opportunities to describe and understand ecosystem functioning. Ecological networks describe interactions between species, the underlying structure of communities and the function and stability of ecosystems. They provide the ability to assess the robustness of complex ecological communities to species loss, as well as a novel way of guiding restoration. However, empirically quantifying the interactions between entire communities remains a significant challenge. 2. Concomitantly, advances in DNA sequencing technologies are resolving previously intractable questions in functional and taxonomic biodiversity and provide enormous potential to determine hitherto difficult to observe species interactions. Combining DNA metabarcoding approaches with ecological network analysis presents important new opportunities for understanding large-scale ecological and evolutionary processes, as well as providing powerful tools for building ecosystems that are resilient to environmental change. 3. We propose a novel ‘nested tagging’ metabarcoding approach for the rapid construction of large, phylogenetically structured species-interaction networks. Taking tree–insect–parasitoid ecological networks as an illustration, we show how measures of network robustness, constructed using DNA metabarcoding, can be used to determine the consequences of tree species loss within forests, and forest habitat loss within wider landscapes. By determining which species and habitats are important to network integrity, we propose new directions for forest management. 4. Merging metabarcoding with ecological network analysis provides a revolutionary opportunity to construct some of the largest, phylogenetically structured species-interaction networks to date, providing new ways to: (i) monitor biodiversity and ecosystem functioning; (ii) assess the robustness of interacting communities to species loss; and (iii) build ecosystems that are more resilient to environmental change

Romantic Nationalism, Thomas De Quincey and the Public Debate about the First Opium War, 1839-42

This essay situates Thomas De Quincey's essay 'On the Opium and the China Question' published in Blackwood's Edinburgh Magazine in June 1840 within the British public debate about the politics of the opium trade with China and the First Opium War. The essay argues that this war was one that involved a series of romantic period literary personalities, including De Quincey, T. B. Macaulay, Samuel Warren, Algernon Thelwall (son of the radical 1790s politician John Thelwall), and John Cam Hobhouse. De Quincey emerges as both an idiosyncratic, though public voice, and as a character, 'the opium eater', that is frequently invoked by participants in the debate

Combining 3D printing and liquid handling to produce user-friendly reactionware for chemical synthesis and purification

We use two 3D-printing platforms as solid- and liquid-handling fabricators, producing sealed reactionware for chemical synthesis with the reagents, catalysts and purification apparatus integrated into monolithic devices. Using this reactionware, a multi-step reaction sequence was performed by simply rotating the device so that the reaction mixture flowed through successive environments under gravity, without the need for any pumps or liquid-handling prior to product retrieval from the reactionware in a pure form