A genus six cyclic tetragonal reduction of the Benney equations

A reduction of Benney’s equations is constructed corresponding to Schwartz–Christoffel maps associated with a family of genus six cyclic tetragonal curves. The mapping function, a second kind Abelian integral on the associated Riemann surface, is constructed explicitly as a rational expression in derivatives of the Kleinian σ-function of the curve

Morphological heterogeneity of HeLa cell mitochondria visualized by a modified diaminobenzidine staining technique

The diaminobenzidine (DAB) technique for the ultrastructural localization of sites of cytochrome c oxidase activity in animal tissues has been adapted to the visualization of mitochondria in animal cells growing in culture. The modified technique allows the staining of mitochondria in all cells in coverslip preparatins for light microscopy. Electron microscopy of thin sections of material treated by this method has revealed that all mitochondrial profiles within a cell (and only these) are stained and they exhibit a well preserved size and internal structure. Coverslip cultures of synchronized and unsynchronized HeLa (F-315) cells stained with the DAB reaction were examined under oil immersion. In the majority of the cells, mitochondria were recognized as discrete bodies in the thinner peripheral portion of the cytoplasm. This observation indicates that in a large proportion of HeLa F-315 cells, at least under the growth conditions used here, the mitochondrial complement is dividied into distinct organelles. This examination also revealed a considerable morphological heterogeneity of mitochondria, which exhibited an ovoid or short rod-like or, less frequently, long filamentous shape, with some evidence of branching. The variability in mitochondrial morphology appeared to be far more prounced between different cells than within individual cells; this cellular heterogeneity was not related in any obvious way to cell-cycle-dependent changes

The Effect of Vincristine Sulphate on the Axoplasmic Flow of Proteins in Cultured Sympathetic Neurons

The effect of vincristine sulphate on the axoplasmic flow of labelled proteins in neurites of chick embryo sympathetic neurons growing in tissue culture was studied by autoradiography. In control neurons most of the 3H-proteins synthesized during a 90-min pulse with a 3H-amino acid were localized in cell bodies. There was a diminishing gradient of labelled proteins in the neurites which was highest in portions adjacent to the cell bodies and lowest at the periphery. During a physiological chase there was a gradual increase in the amount of label in the neurites, so that after a 15-h chase even the most peripheral portions were well labelled. This indicates that a portion of the labelled proteins synthesized in the cell bodies are transported peripherally into the neurites. The centrifugal movement of labelled proteins in neurites was markedly decreased when cells were grown in medium containing 10 µg/ml vincristine sulphate. After a 15-h chase in the presence of drug only a small amount of label was in the peripheral portion of the neurites. Treatment with vincristine did not decrease the rate of amino acid incorporation or alter the rate of protein turnover during the course of the experiment. Thus an explanation of the results based on an altered rate of total cell protein synthesis or degradation is unlikely. The capacity of sympathetic neurons to take up and concentrate exogenous [3H]norepinephrine in their neurites was only slightly reduced by vincristine. This indicates that at least some cellular activities requiring metabolic energy are relatively unaffected by the interruption in axoplasmic flow caused by vincristine and that the mechanism by which vincristine interferes with axoplasmic flow does not involve general cellular toxicity. The major morphological differences between control and vincristine-treated neurons were the absence of microtubules and the presence of crystal-like structures within the cells. The relationship between the effect of vincristine on the axoplasmic flow of proteins and the arrangement of the microtubule system is discussed

Cylindrical Algebraic Sub-Decompositions

Cylindrical algebraic decompositions (CADs) are a key tool in real algebraic geometry, used primarily for eliminating quantifiers over the reals and studying semi-algebraic sets. In this paper we introduce cylindrical algebraic sub-decompositions (sub-CADs), which are subsets of CADs containing all the information needed to specify a solution for a given problem. We define two new types of sub-CAD: variety sub-CADs which are those cells in a CAD lying on a designated variety; and layered sub-CADs which have only those cells of dimension higher than a specified value. We present algorithms to produce these and describe how the two approaches may be combined with each other and the recent theory of truth-table invariant CAD. We give a complexity analysis showing that these techniques can offer substantial theoretical savings, which is supported by experimentation using an implementation in Maple.Comment: 26 page

Unmasking quality: exploring meanings of health by doing art

This paper arises from a presentation at the ‘Quality in Healthcare’ symposium at Cumberland Lodge, England, in 2013. MK, CR and SH conceived the paper and led the writing of the manuscript. JF, JL-D, AC, DE contributed substantially to the intellectual content of the paper through providing critical commentary and interpretation. All authors read and approved the final manuscript

Interplay of local hydrogen-bonding and long-ranged dipolar forces in simulations of confined water

Spherical truncations of Coulomb interactions in standard models for water permit efficient molecular simulations and can give remarkably accurate results for the structure of the uniform liquid. However truncations are known to produce significant errors in nonuniform systems, particularly for electrostatic properties. Local molecular field (LMF) theory corrects such truncations by use of an effective or restructured electrostatic potential that accounts for effects of the remaining long-ranged interactions through a density-weighted mean field average and satisfies a modified Poisson's equation defined with a Gaussian-smoothed charge density. We apply LMF theory to three simple molecular systems that exhibit different aspects of the failure of a naive application of spherical truncations -- water confined between hydrophobic walls, water confined between atomically-corrugated hydrophilic walls, and water confined between hydrophobic walls with an applied electric field. Spherical truncations of 1/r fail spectacularly for the final system in particular, and LMF theory corrects the failings for all three. Further, LMF theory provides a more intuitive way to understand the balance between local hydrogen bonding and longer-ranged electrostatics in molecular simulations involving water.Comment: Submitted to PNA

Deriving bases for Abelian functions

We present a new method to explicitly define Abelian functions associated with algebraic curves, for the purpose of finding bases for the relevant vector spaces of such functions. We demonstrate the procedure with the functions associated with a trigonal curve of genus four. The main motivation for the construction of such bases is that it allows systematic methods for the derivation of the addition formulae and differential equations satisfied by the functions. We present a new 3-term 2-variable addition formulae and a complete set of differential equations to generalise the classic Weierstrass identities for the case of the trigonal curve of genus four.Comment: 35page

Do people with intellectual disabilities understand their prescription medication? A scoping review

© 2019 The Authors. Journal of Applied Research in Intellectual Disabilities Published by John Wiley & Sons Ltd.Background: People with intellectual disabilities are more likely to experience poor health than the general population and are frequently prescribed multiple medications. Therefore, it is important that people with intellectual disabilities understand their medication and potential adverse effects. Method: A scoping review explored people with intellectual disabilities' knowledge of prescription medications, their risks and how medication understanding can be improved. Results: Ten journal articles were included. People with intellectual disabilities often lacked understanding of their medication, including its name, purpose and when and how to take it. Participants were often confused or unaware of adverse effects associated with their medication. Information was sometimes explained to carers rather than people with intellectual disabilities. Some interventions and accessible information helped to improve knowledge in people with intellectual disabilities. Conclusion: There is a need for accessible and tailored information about medication to be discussed with people with intellectual disabilities in order to meet legal and best practice standards.Peer reviewe