The rigidity of infinite graphs

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and Henneberg combinatorial characterisations of generic infinitesimal rigidity for finite graphs in the Euclidean plane. Also Tay's multi-graph characterisation of the rigidity of generic finite body-bar frameworks in d-dimensional Euclidean space is generalised to the non-Euclidean l^p norms and to countably infinite graphs. For all dimensions and norms it is shown that a generically rigid countable simple graph is the direct limit of an inclusion tower of finite graphs for which the inclusions satisfy a relative rigidity property. For d>2 a countable graph which is rigid for generic placements in R^d may fail the stronger property of sequential rigidity, while for d=2 the equivalence with sequential rigidity is obtained from the generalised Laman characterisations. Applications are given to the flexibility of non-Euclidean convex polyhedra and to the infinitesimal and continuous rigidity of compact infinitely-faceted simplicial polytopes.Comment: 51 page

A portable 3D printer system for the diagnosis and treatment of multidrug-resistant bacteria

Summary: Multidrug-resistant bacteria are a major threat to human health, but broad-spectrum antibiotics are losing efficacy. There is a need to screen a given drug against a bacterial infection outside of the laboratory. To address this need, we have designed and built an inexpensive and easy-to-use 3D-printer-based system that allows easily readable quantitative tests for the performance of antibacterial drugs. The platform creates a sterile diagnostic device by using 3D printing, and the device is filled automatically with growth medium, and then antibiotics are sprayed onto the medium by ink-jet technology. The sample for testing can be introduced via a fluid port, and the printer hot bed is used to incubate the device, allowing operation in the field. Combining advantages from various established tests of antibacterial performance, this allows the comparison of a specific antibiotics and bacteria. Also, this system can create and test several antibiotic formulations for therapeutic use, and we demonstrate this potential by investigating a mixture of pathogens that are only killed by a mixture of drugs

Digitization of multistep organic synthesis in reactionware for on-demand pharmaceuticals

Chemical manufacturing is often done at large facilities that require a sizable capital investment and then produce key compounds for a finite period. We present an approach to the manufacturing of fine chemicals and pharmaceuticals in a self-contained plastic reactionware device. The device was designed and constructed by using a chemical to computer-automated design (ChemCAD) approach that enables the translation of traditional bench-scale synthesis into a platform-independent digital code. This in turn guides production of a three-dimensional printed device that encloses the entire synthetic route internally via simple operations. We demonstrate the approach for the γ-aminobutyric acid receptor agonist, (±)-baclofen, establishing a concept that paves the way for the local manufacture of drugs outside of specialist facilities

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

Hypoxia and hyperglycaemia determine why some endometrial tumours fail to respond to metformin

High expression of Ki67, a proliferation marker, is associated with reduced endometrial cancer-specific survival. Pre-surgical metformin reduces tumour Ki-67 expression in some women with endometrial cancer. Metformin's anti-cancer activity may relate to effects on cellular energy metabolism. Since tumour hypoxia and glucose availability are major cellular redox determinants, we evaluated their role in endometrial cancer response to metformin. Endometrial cancer biopsies from women treated with pre-surgical metformin were tested for the hypoxia markers, HIF-1α and CA-9. Endometrial cancer cell lines were treated with metformin in variable glucose concentrations in normoxia or hypoxia and cell viability, mitochondrial biogenesis, function and energy metabolism were assessed. In women treated with metformin (n = 28), Ki-67 response was lower in hypoxic tumours. Metformin showed minimal cytostatic effects towards Ishikawa and HEC1A cells in conventional medium (25 mM glucose). In low glucose (5.5 mM), a dose-dependent cytostatic effect was observed in normoxia but attenuated in hypoxia. Tumours treated with metformin showed increased mitochondrial mass (n = 25), while in cultured cells metformin decreased mitochondrial function. Metformin targets mitochondrial respiration, however, in hypoxic, high glucose conditions, there was a switch to glycolytic metabolism and decreased metformin response. Understanding the metabolic adaptations of endometrial tumours may identify patients likely to derive clinical benefit from metformin

The challenges of communicating research evidence in practice: perspectives from UK health visitors and practice nurses

&lt;p&gt;Background: Health practitioners play a pivotal role in providing patients with up-to-date evidence and health information. Evidence-based practice and patient-centred care are transforming the delivery of healthcare in the UK. Health practitioners are increasingly balancing the need to provide evidence-based information against that of facilitating patient choice, which may not always concur with the evidence base. There is limited research exploring how health practitioners working in the UK, and particularly those more autonomous practitioners such as health visitors and practice nurses working in community practice settings, negotiate this challenge. This research provides a descriptive account of how health visitors and practice nurses negotiate the challenges of communicating health information and research evidence in practice.&lt;/p&gt; &lt;p&gt;Methods: A total of eighteen in-depth telephone interviews were conducted in the UK between September 2008 and May 2009. The participants comprised nine health visitors and nine practice nurses, recruited via adverts on a nursing website, posters at a practitioner conference and through recommendation. Thematic analysis, with a focus on constant comparative method, was used to analyse the data.&lt;/p&gt; &lt;p&gt;Results: The data were grouped into three main themes: communicating evidence to the critically-minded patient; confidence in communicating evidence; and maintaining the integrity of the patient-practitioner relationship. These findings highlight some of the daily challenges that health visitors and practice nurses face with regard to the complex and dynamic nature of evidence and the changing attitudes and expectations of patients. The findings also highlight the tensions that exist between differing philosophies of evidence-based practice and patient-centred care, which can make communicating about evidence a daunting task.&lt;/p&gt; &lt;p&gt;Conclusions: If health practitioners are to be effective at communicating research evidence, we suggest that more research and resources need to be focused on contextual factors, such as how research evidence is negotiated, appraised and communicated within the dynamic patient-practitioner relationship.&lt;/p&gt

3D designed and printed chemical generators for on demand reagent synthesis

Modern science has developed well-defined and versatile sets of chemicals to perform many specific tasks, yet the diversity of these reagents is so large that it can be impractical for any one lab to stock everything they might need. At the same time, isssues of stability or limited supply mean these chemicals can be very expensive to purchase from specialist retailers. Here, we address this problem by developing a cartridge -oriented approach to reactionware-based chemical generators which can easily and reliably produce specific reagents from low-cost precursors, requiring minimal expertise and time to operate, potentially in low infrastructure environments. We developed these chemical generators for four specific targets; transition metal catalyst precursor tris(dibenzylideneacetone)dipalladium(0) [Pd2(dba)3], oxidising agent Dess-Martin periodinane (DMP), protein photolinking reagent succinimidyl 4,4’-azipentanoate (NHS-diazirine), and the polyoxometalate cluster {P8W48}. The cartridge synthesis of these materials provides high-quality target compounds in good yields which are suitable for subsequent utilization

Continuous parallel ESI-MS analysis of reactions carried out in a bespoke 3D printed device

Herein, we present an approach for the rapid, straightforward and economical preparation of a tailored reactor device using three-dimensional (3D) printing, which can be directly linked to a high-resolution electrospray ionisation mass spectrometer (ESI-MS) for real-time, in-line observations. To highlight the potential of the setup, supramolecular coordination chemistry was carried out in the device, with the product of the reactions being recorded continuously and in parallel by ESI-MS. Utilising in-house-programmed computer control, the reactant flow rates and order were carefully controlled and varied, with the changes in the pump inlets being mirrored by the recorded ESI-MS spectra

The rigidity of infinite graphs

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in the normed spaces (\bR^d,\|\cdot \|_q), for $d\geq 2$ and $1 <q < \infty$. Generalisations are obtained for the Laman combinatorial characterisation of generic infinitesimal rigidity for  finite graphs in  (\bR^2,\|\cdot \|_2).  Also Tay's multi-graph characterisation of generic infinitesimal rigidity for finite body-bar frameworks in (\bR^d,\|\cdot\|_2) is generalised to the non-Euclidean norms and to countably infinite graphs. For all dimensions and norms  it is shown that a generically rigid countable simple graph is the direct limit $G= \varinjlim G_k$ of an inclusion tower of finite graphs $G_1 \subseteq G_2 \subseteq  \dots$ for which the inclusions satisfy a relative rigidity property. For $d\geq 3$ a countable graph which is rigid for generic placements in  \bR^d may fail the stronger property of  sequential rigidity, while for $d=2$ the properties are equivalent