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

Influence of Ethnicity, Gender and Answering Mode on a Virtual Point-to-Origin Task

In a virtual point-to-origin task, participants seem to show&nbsp;different response patterns and underlying strategies for orientation, such&nbsp;as ”turner” and ”non-turner” response patterns. Turners respond as if&nbsp;succeeding to update simulated heading changes, and non-turners respond as if&nbsp;failing to update their heading, resulting in left-right hemisphere errors.&nbsp;We present two other response patterns, ”non-movers” and ”spinners”,&nbsp;that also appear to result in failures to update heading. We have three&nbsp;specific goals in mind: (1) extend previous findings of higher turner rates&nbsp;with spatial language response mode using a point-to-origin task instead of a&nbsp;triangle completion task; (2) replicate the gender effect of males more&nbsp;likely responding as turners; (3) examine ethnicity influence. Designed as a&nbsp;classroom study, we presented participants (N = 498) with four passages&nbsp;through a virtual star field. Participants selected the direction pointing to&nbsp;the origin from four multiple-choice items. Response mode was either&nbsp;pictograms or written lan- guage, chosen to compare with similar studies and&nbsp;see if these response modes have an effect on virtual orientation behaviour.&nbsp;Results show a majority of participants (48.35%) classified as non-turners,&nbsp;32.93% turners, 15.57% as non-movers, and 3.14% as spinners. A multinomial&nbsp;regression model reached 49% classification performance. Written spatial&nbsp;language, compared to pictograms, made turner response patterns more likely;&nbsp;this effect was more pronounced for Chinese participants and among females,&nbsp;but not male Caucasians. Moreover, higher turner numbers for written spatial&nbsp;language extends Avraamides findings of higher turner numbers when&nbsp;participants turned their bodies toward the origin but not when they&nbsp;responded verbally. Using pictorial response mode (i.e., top-down picture of&nbsp;a head) may have increased cognitive load because it could be considered more&nbsp;embodied. It remains to be seen how we can reduce the reference frame&nbsp;conflict that might have caused increased cognitive load. Second, our results&nbsp;are inconsistent with previous research in that males overall did not show&nbsp;more turner behaviour than females. Future research may look at possible&nbsp;underlying factors, such as cultural norms. Third, individualistic cultures&nbsp;(Caucasians) [Greif, 1994] lean towards turner response patterns, whereas&nbsp;collectivist cultures lean towards non-turner response patterns

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

New Labour and work-time regulation: a Marxian analysis of the UK economy

This paper examines the impact of work-time regulation, introduced by the UK's New Labour governments (1997 to 2010). In doing so, we return to Marx's hypotheses regarding the length of the working day. These include the arguments that class conflict over the length of the working day is inherently distributional in a surplus-value sense and that workers often display a preference for reduced hours even with a proportionate reduction in pay. Our quantitative Marxist methodology provides a way of assessing the pattern of surplus-value before and during the period of office of the New Labour governments and the distributional effects of regulation. The impact of such regulations on workers' preferences are examined through an investigation of British Household Panel Survey data. Although many have been sceptical concerning the record of the last Labour governments, policies such as the Working Time Regulations (1998) and the Work-Life Balance Campaign (2000) are found to have been noteworthy innovations in the labour market. This is all the more important given recent moves by the successor government to weaken work-time regulation. Our results suggest the impact of these policy initiatives was broadly favourable, though the effect on men and women was different