Finite and infinitesimal rigidity with polyhedral norms

We characterise finite and infinitesimal rigidity for bar-joint frameworks in R^d with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be equivalent for finite frameworks in R^d which are well-positioned with respect to P. An edge-labelling determined by the facets of the unit ball and placement of the framework is used to characterise infinitesimal rigidity in R^d in terms of monochrome spanning trees. An analogue of Laman's theorem is obtained for all polyhedral norms on R^2.Comment: 26 page

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

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

Computer simulation of protein systems

Ligand binding to dihydrofolate reductase (DHFR) is discussed. This is an extremely important enzyme, as it is the target of several drugs (inhibitors) which are used clinically as antibacterials, antiprotozoals and in cancer chemotherapy. DHFR catalyzes the NADPH (reduced nicotinamide adenine dinucleotide phosphate) dependent reduction of dihydrofolate to tetrahydrofolate, which is used in several pathways of purine and pyrimidine iosynthesis, including that of thymidylate. Since DNA synthesis is dependent on a continuing supply of thymidylate, a blockade of DHFR resulting in a depletion of thymidylate can lead to the cessation of growth of a rapidly proliferating cell line. DHFR exhibits a significant species to species variability in its sensitivity to various inhibitors. For example, trimethoprim, an inhibitor of DHFR, binds to bacterial DHFR's 5 orders of magnitude greater than to vertebrate DHFR's. The structural mechanics, dynamics and energetics of a family of dihydrofolate reductases are studied to rationalize the basis for the inhibitor of these enyzmes and to understand the molecular basis of the difference in the binding constants between the species. This involves investigating the conformational changes induced in the protein on binding the ligand, the internal strain imposed by the enzyme on the ligand, the restriction of fluctuations in atom positions due to binding and the consequent change in entropy

The dissolution and solid-state behaviours of coground ibuprofen–glucosamine HCl

The cogrinding technique is one of most effective methods for improving the dissolution of poorly water-soluble drugs and it is superior to other approaches from an economical as well as an environmental standpoint, as the technique does not require any toxic organic solvents. Present work explores the role of d-glucosamine HCl (GL) as a potential excipient to improve dissolution of a low melting point drug, ibuprofen (Ibu), using physical mixtures and coground formulations. The dissolution of the poorly soluble drug has been improved by changing the ratio of Ibu:GL and also grinding time. The results also showed that although GL can enhance the solubility of Ibu, it also reduces pH around the Ibu particles which led to poor dissolution performance when the concentration of GL is high. The effect of GL on the solubility of Ibu could be misleading if the pH of the final solution was not measured. Grinding reduced the particle size of GL significantly but in case of Ibu it was less effective. Solid state analysis (XRPD, DSC, and FT-IR) showed that ibuprofen is stable under grinding conditions, but the presence of high concentration of GL in samples subjected to high grinding times caused changes in FT-IR spectrum of Ibu which could be due to intermolecular hydrogen bond or esterification between the carboxylic acid group in the ibuprofen and hydroxyl group in the GL

Gluon flux-tube distribution and linear confinement in baryons

We have observed the formation of gluon flux-tubes within baryons using lattice QCD techniques. A high-statistics approach, based on translational and rotational symmetries of the four-dimensional lattice, enables us to observe correlations between vacuum action density and quark positions in a completely gauge independent manner. This contrasts with earlier studies which used gauge-dependent smoothing techniques. We used 200 O(a^2) improved quenched QCD gauge-field configurations on a 16^3x32 lattice with a lattice spacing of 0.123 fm. In the presence of static quarks flux tubes representing the suppression of gluon-field fluctuations are observed. We have analyzed 11 L-shapes and 8 T and Y shapes of varying sizes in order to explore a variety of flux-tube topologies, including the ground state. At large separations, Y-shape flux-tube formation is observed. T-shaped paths are observed to relax towards a Y-shaped topology, whereas L-shaped paths give rise to a large potential energy. We do not find any evidence for the formation of a Delta-shaped flux-tube (empty triangle) distribution. However, at small quark separations, we observe an expulsion of gluon-field fluctuations in the shape of a filled triangle with maximal expulsion at the centre of the triangle. Having identified the precise geometry of the flux distribution, we are able to perform quantitative comparison between the length of the flux-tube and the associated static quark potential. For every source configuration considered we find a universal string tension, and conclude that, for large quark separations, the ground state potential is that which minimizes the length of the flux-tube. The flux tube radius of the baryonic ground state potential is found to be 0.38 \pm 0.03 fm, with vacuum fluctuations suppressed by 7.2 \pm 0.6 %.Comment: 16 pages, final version as accepted for publication in Physical review D1. Abstract, text, references and some figures have been revise

Linoleic acid participates in the response to ischemic brain injury through oxidized metabolites that regulate neurotransmission.

Linoleic acid (LA; 18:2 n-6), the most abundant polyunsaturated fatty acid in the US diet, is a precursor to oxidized metabolites that have unknown roles in the brain. Here, we show that oxidized LA-derived metabolites accumulate in several rat brain regions during CO2-induced ischemia and that LA-derived 13-hydroxyoctadecadienoic acid, but not LA, increase somatic paired-pulse facilitation in rat hippocampus by 80%, suggesting bioactivity. This study provides new evidence that LA participates in the response to ischemia-induced brain injury through oxidized metabolites that regulate neurotransmission. Targeting this pathway may be therapeutically relevant for ischemia-related conditions such as stroke

The economic and innovation contribution of universities: a regional perspective

Universities and other higher education institutions (HEIs) have come to be regarded as key sources of knowledge utilisable in the pursuit of economic growth. Although there have been numerous studies assessing the economic and innovation impact of HEIs, there has been little systematic analysis of differences in the relative contribution of HEIs across regions. This paper provides an exploration of some of these differences in the context of the UK’s regions. Significant differences are found in the wealth generated by universities according to regional location and type of institution. Universities in more competitive regions are generally more productive than those located in less competitive regions. Also, traditional universities are generally more productive than their newer counterparts, with university productivity positively related to knowledge commercialisation capabilities. Weaker regions tend to be more dependent on their universities for income and innovation, but often these universities under-perform in comparison to counterpart institutions in more competitive regions. It is argued that uncompetitive regions lack the additional knowledge infrastructure, besides universities, that are more commonly a feature of more competitive regions