Acid polishing of lead glass

Purpose: The polishing of cut lead glass crystal is effected through the dowsing of the glass in a mixture of two separate acids, which between them etch the surface and as a result cause it to be become smooth. In order to characterise the resultant polishing the rate of surface etching must be known, but when this involves multicomponent surface reactions it becomes unclear what this rate actually is. Methods: We develop a differential equation based discrete model to determine the effective etching rate by means of an atomic scale model of the etching process. Results: We calculate the etching rate numerically and provide an approximate asymptotic estimate. Conclusions: The natural extension of this work would be to develop a continuum advection-diffusion model

Competition-induced criticality in a model of meme popularity

Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent alph

Accuracy of mean-field theory for dynamics on real-world networks

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of such theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4

Competition-induced criticality in a model of meme popularity

Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the system at criticality. The popularity growth of each meme is described by a critical branching process, and asymptotic analysis predicts power-law distributions of popularity with very heavy tails (exponent alph

Accuracy of mean-field theory for dynamics on real-world networks

Mean-field analysis is an important tool for understanding dynamics on complex networks. However, surprisingly little attention has been paid to the question of whether mean-field predictions are accurate, and this is particularly true for real-world networks with clustering and modular structure. In this paper, we compare mean-field predictions to numerical simulation results for dynamical processes running on 21 real-world networks and demonstrate that the accuracy of such theory depends not only on the mean degree of the networks but also on the mean first-neighbor degree. We show that mean-field theory can give (unexpectedly) accurate results for certain dynamics on disassortative real-world networks even when the mean degree is as low as 4

Airway Elastin is increased in severe asthma and relates to proximal wall area: histological and computed tomography findings from the U-BIOPRED severe asthma study

Background: Airway remodelling, which may include goblet cell hyperplasia / hypertrophy, changes in epithelial integrity, accumulation of extracellular matrix components, smooth muscle hypertrophy and thickening of the lamina reticularis, is a feature of severe asthma and contributes to the clinical phenotype. Objective: Within the U-BIOPRED severe asthma study, we have assessed histological elements of airway remodelling and their relationship to computed tomography (CT) measures of proximal airway dimensions. Methods: Bronchial biopsies were collected from two severe asthma groups, one non-smoker (SAn, n = 28) and one current/ex-smoker (SAs/ex, n = 13), and a mild-moderate asthma group (MMA, n = 28) classified and treated according to GINA guidelines, plus a healthy control group (HC, n = 33). Movat's pentachrome technique was used to identify mucin, elastin and total collagen in these biopsies. The number of goblet cells (mucin+) was counted as a percentage of the total number of epithelial cells and the percentage mucin epithelial area measured. The percentage area of elastic fibres and total collagen within the submucosa was also measured, and the morphology of the elastic fibres classified. Participants in the asthma groups also had a CT scan to assess large airway morphometry. Results: The submucosal tissue elastin percentage was higher in both severe asthma groups (16.1% SAn, 18.9% SAs/ex) compared with the HC (9.7%) but did not differ between asthma groups. There was a positive relationship between elastin and airway wall area measured by CT (n = 18–20, rho=0.544, p = 0.024), which also related to an increase in elastic fibres with a thickened lamellar morphological appearance. Mucin epithelial area and total collagen were not different between the four groups. Due to small numbers of suitable CT scans, it was not feasible to compare airway morphometry between the asthma groups. Conclusion: These findings identify a link between extent of elastin deposition and airway wall thickening in severe asthma