Competitive versions of vertex ranking and game acquisition, and a problem on proper colorings

In this thesis we study certain functions on graphs. Chapters 2 and 3 deal with variations on vertex ranking, a type of node-labeling scheme that models a parallel processing problem. A k-ranking of a graph G is a labeling of its vertices from {1,...,k} such that any nontrivial path whose endpoints have the same label contains a vertex with a larger label. In Chapter 2, we investigate the problem of list ranking, wherein every vertex of G is assigned a set of possible labels, and a ranking must be constructed by labeling each vertex from its list; the list ranking number of G is the minimum k such that if every vertex is assigned a set of k possible labels, then G is guaranteed to have a ranking from these lists. We compute the list ranking numbers of paths, cycles, and trees with many leaves. In Chapter 3, we investigate the problem of on-line ranking, which asks for an algorithm to rank the vertices of G as they are revealed one at a time in the subgraph of G induced by the vertices revealed so far. The on-line ranking number of G is the minimum over all such labeling algorithms of the largest label that the algorithm can be forced to use. We give algorithmic bounds on the on-line ranking number of trees in terms of maximum degree, diameter, and number of internal vertices. Chapter 4 is concerned with the connectedness and Hamiltonicity of the graph G^j_k(H), whose vertices are the proper k-colorings of a given graph H, with edges joining colorings that differ only on a set of vertices contained within a connected subgraph of H on at most j vertices. We introduce and study the parameters g_k(H) and h_k(H), which denote the minimum j such that G^j_k(H) is connected or Hamiltonian, respectively. Finally, in Chapter 5 we compute the game acquisition number of complete bipartite graphs. An acquisition move in a weighted graph G consists a vertex v taking all the weight from a neighbor whose weight is at most the weight of v. In the acquisition game on G, each vertex initially has weight 1, and players Min and Max alternate acquisition moves until the set of vertices remaining with positive weight is an independent set. Min seeks to minimize the size of the final independent set, while Max seeks to maximize it; the game acquisition number is the size of the final set under optimal play

Resonance assignments for latherin, a natural surfactant protein from horse sweat

Latherin is an intrinsically surfactant protein of ~23 kDa found in the sweat and saliva of horses. Its function is probably to enhance the translocation of sweat water from the skin to the surface of the pelt for evaporative cooling. Its role in saliva may be to enhance the wetting, softening and maceration of the dry, fibrous food for which equines are adapted. Latherin is unusual in its relatively high content of aliphatic amino acids (~25 % leucines) that might contribute to its surfactant properties. Latherin is related to the palate, lung, and nasal epithelium carcinoma-associated proteins (PLUNCs) of mammals, at least one of which is now known to exhibit similar surfactant activity to latherin. No structures of any PLUNC protein are currently available. 15N,13C-labelled recombinant latherin was produced in Escherichia coli, and essentially all of the resonances were assigned despite the signal overlap due to the preponderance of leucines. The most notable exceptions include a number of residues located in an apparently dynamic loop region between residues 145 and 154. The assignments have been deposited with BMRB accession number 19067

The structure of latherin, a surfactant allergen protein from horse sweat and saliva

Latherin is a highly surface-active allergen protein found in the sweat and saliva of horses and other equids. Its surfactant activity is intrinsic to the protein in its native form, and is manifest without associated lipids or glycosylation. Latherin probably functions as a wetting agent in evaporative cooling in horses, but it may also assist in mastication of fibrous food as well as inhibition of microbial biofilms. It is a member of the PLUNC family of proteins abundant in the oral cavity and saliva of mammals, one of which has also been shown to be a surfactant and capable of disrupting microbial biofilms. How these proteins work as surfactants while remaining soluble and cell membrane-compatible is not known. Nor have their structures previously been reported. We have used protein nuclear magnetic resonance spectroscopy to determine the conformation and dynamics of latherin in aqueous solution. The protein is a monomer in solution with a slightly curved cylindrical structure exhibiting a ‘super-roll’ motif comprising a four-stranded anti-parallel β-sheet and two opposing α-helices which twist along the long axis of the cylinder. One end of the molecule has prominent, flexible loops that contain a number of apolar amino acid side chains. This, together with previous biophysical observations, leads us to a plausible mechanism for surfactant activity in which the molecule is first localized to the non-polar interface via these loops, and then unfolds and flattens to expose its hydrophobic interior to the air or non-polar surface. Intrinsically surface-active proteins are relatively rare in nature, and this is the first structure of such a protein from mammals to be reported. Both its conformation and proposed method of action are different from other, non-mammalian surfactant proteins investigated so far

Addressing challenges in gaining informed consent for a research study investigating falls in people with intellectual disability

Background: People with intellectual disability encounter multiple barriers to accessing quality, evidence based health care which is detrimental to their quality of life (Qol) and mortality. Engaging people with intellectual disability when conducting research is vital to address these QoL issues. People with intellectual disability have the right to engage in research pertinent to them but at present, they are under-represented in research and there are limited methods available to ensure that people with intellectual disability are fully supported to provide informed consent. Therefore the aim of this paper is to describe an informed consent process and reflect on the methods used when recruiting persons with intellectual disability 1 for a research study which is currently investigating falls among people with intellectual disability. Methods: A systematic and holistic consent procedure, underpinned by ethical guidelines, was developed and used alongside recommended strategies to engage people with intellectual disability in a research study. Results: Only three participants (7.5%) were deemed capable of consenting independently, while 37 participants (92.5%) required the support of a proxy. Of these 37 participants, 22 participated in the consent process, while 15 depended mainly on their caregiver to make decisions for them. Adapted communication strategies were found to facilitate a person who has an intellectual disability\u27s participation in the consent procedure. The adapted written information sheets were of secondary importance. Conclusion: The consent procedure was a respectful means of determining a person\u27s capacity to consent and indicating where there was a need for proxy consent. Appropriate communication strategies and the inclusion of familiar caregiver(s) were critical components for facilitating the person with an intellectual disability to participate in the consent procedure

Seasonal and spatial dynamics of enteric viruses in wastewater and in riverine and estuarine receiving waters

Enteric viruses represent a global public health threat and are implicated in numerous foodborne and waterborne disease outbreaks. Nonetheless, relatively little is known of their fate and stability in the environment. In this study we used carefully validated methods to monitor enteric viruses, namely adenovirus (AdV), JC polyomavirus (JCV), noroviruses (NoVs), sapovirus (SaV) and hepatitis A and E viruses (HAV and HEV) from wastewater source to beaches and shellfish beds. Wastewater influent and effluent, surface water, sediment and shellfish samples were collected in the Conwy catchment (North Wales, UK) once a month for one year. High concentrations of AdV and JCV were found in the majority of samples, and no seasonal patterns were observed. No HAV and HEV were detected and no related illnesses were reported in the area during the period of sampling. Noroviruses and SaV were also detected at high concentrations in wastewater and surface water, and their presence correlated with local gastroenteritis outbreaks during the spring and autumn seasons. Noroviruses were also found in estuarine sediment and in shellfish harvested for human consumption. As PCR-based methods were used for quantification, viral infectivity and degradation was estimated using a NoV capsid integrity assay. The assay revealed low-levels of viral decay in wastewater effluent compared to influent, and more significant decay in environmental waters and sediment. Results suggest that AdV and JCV may be suitable markers for the assessment of the spatial distribution of wastewater contamination in the environment; and pathogenic viruses can be directly monitored during and after reported outbreaks to prevent further environment-derived illnesses

Shining a Light on s-Triazine-Based Polymers

The strong interplay between the structure and optical properties of conjugated s-triazine-based framework (CTF) materials is explored in a combined experimental and computational study. The experimental absorption and fluorescence spectra of the CTF-1 material, a polymer obtained through the trimerization of 1,4-dicyanobenzene, are compared with the results of time-dependent density functional theory and approximate coupled cluster theory (CC2) calculations on cluster models of the polymer. To help explain the polymer data, we compare its optical properties with those measured and predicted for the 2,4,6-triphenyl-1,3,5-triazine model compound. Our analysis shows that CTFs, in line with experimental diffraction data, are likely to be layered materials based around flat hexagonal-like sheets and suggests that the long-wavelength part of the CTF-1 absorption spectrum displays a pronounced effect of stacking. Red-shifted peaks in the absorption spectrum appear that are absent for an isolated sheet. We also show that the experimentally observed strong fluorescence of CTF-1 and other CTF materials is further evidence of the presence of rings in the layers, as structures without rings are predicted to have extremely long excited state lifetimes and hence would display negligible fluorescence intensities. Finally, subtle differences between the experimental absorption spectra of CTF-1 samples prepared using different synthesis routes are shown to potentially arise from different relative arrangements of stacked layers

Mesh inlay, mesh kit or native tissue repair for women having repeat anterior or posterior prolapse surgery: randomised controlled trial (PROSPECT)

Funding The project was funded by the National Institute for Health Research Health Technology Assessment Programme (Project Number 07/60/18). The Health Services Research Unit and the Health Economics Research Unit are funded by the Chief Scientist Office of the Scottish Government Health and Social Care Directorates. Acknowledgements The authors wish to thank the women who participated in the PROSPECT study. We also thank Margaret MacNeil for her secretarial support and data management; Dawn McRae and Lynda Constable for their trial management support; the programming team in CHaRT, led by Gladys McPherson; members of the Project Management Group for their ongoing advice and support of the study; and the staff at the recruitment sites who facilitated the recruitment, treatment and follow up of study participants.Peer reviewedPublisher PD

The Gibbs-Thomson formula at small island sizes - corrections for high vapour densities

In this paper we report simulation studies of equilibrium features, namely circular islands on model surfaces, using Monte-Carlo methods. In particular, we are interested in studying the relationship between the density of vapour around a curved island and its curvature-the Gibbs-Thomson formula. Numerical simulations of a lattice gas model, performed for various sizes of islands, don't fit very well to the Gibbs-Thomson formula. We show how corrections to this form arise at high vapour densities, wherein a knowledge of the exact equation of state (as opposed to the ideal gas approximation) is necessary to predict this relationship. Exploiting a mapping of the lattice gas to the Ising model one can compute the corrections to the Gibbs-Thomson formula using high field series expansions. We also investigate finite size effects on the stability of the islands both theoretically and through simulations. Finally the simulations are used to study the microscopic origins of the Gibbs-Thomson formula. A heuristic argument is suggested in which it is partially attributed to geometric constraints on the island edge.Comment: 27 pages including 7 figures, tarred, gzipped and uuencoded. Prepared using revtex and espf.sty. To appear in Phys. Rev.