On Mathon's construction of maximal arcs in Desarguesian planes. II

In a recent paper [M], Mathon gives a new construction of maximal arcs which generalizes the construction of Denniston. In relation to this construction, Mathon asks the question of determining the largest degree of a non-Denniston maximal arc arising from his new construction. In this paper, we give a nearly complete answer to this problem. Specifically, we prove that when $m\geq 5$ and $m\neq 9$, the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,1}-map is (\floor {m/2} +1). This confirms our conjecture in [FLX]. For {p,q}-maps, we prove that if $m\geq 7$ and $m\neq 9$, then the largest $d$ of a non-Denniston maximal arc of degree $2^d$ in PG(2,2^m) generated by a {p,q}-map is either \floor {m/2} +1 or \floor{m/2} +2.Comment: 21 page

A stochastic SIR network epidemic model with preventive dropping of edges

A Markovian SIR (Susceptible – Infectious - Recovered) model is considered for the spread of an epidemic on a configuration model network, in which susceptible individuals may take preventive measures by dropping edges to infectious neighbours. An effective degree formulation of the model is used in conjunction with the theory of density dependent population processes to obtain a law of large numbers and a functional central limit theorem for the epidemic as the population size N - ¥, assuming that the degrees of individuals are bounded. A central limit theorem is conjectured for the final size of the epidemic. The results are obtained for both the Molloy–Reed (in which the degrees of individuals are deterministic) and Newman–Strogatz–Watts (in which the degrees of individuals are independent and identically distributed) versions of the configuration model. The two versions yield the same limiting deterministic model but the asymptotic variances in the central limit theorems are greater in the Newman–Strogatz–Watts version. The basic reproduction number R0 and the process of susceptible individuals in the limiting deterministic model, for the model with dropping of edges, are the same as for a corresponding SIR model without dropping of edges but an increased recovery rate, though, when R0 > 1, the probability of a major outbreak is greater in the model with dropping of edges. The results are specialised to the model without dropping of edges to yield conjectured central limit theorems for the final size of Markovian SIR epidemics on configuration-model networks, and for the giant components of those networks. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations are good, even for moderate N

Individual preventive social distancing during an epidemic may have negative population-level outcomes

The outbreak of an infectious disease in a human population can lead to individuals responding with preventive measures in an attempt to avoid getting infected. This leads to changes in contact patterns. However, as we show in this paper, rational behaviour at the individual level, such as social distancing from infectious contacts, may not always be beneficial for the population as a whole. We use epidemic network models to demonstrate the potential negative consequences at the population level. We take into account the social structure of the population through several network models. As the epidemic evolves, susceptible individuals may distance themselves from their infectious contacts. Some individuals replace their lost social connections by seeking new ties. If social distancing occurs at high rates at the beginning of an epidemic, then this can prevent an outbreak from occurring. However, we show that moderate social distancing can worsen the disease outcome, both in the initial phase of an outbreak and the final epidemic size. Moreover, the same negative effect can arise in real-world networks. Our results suggest that one needs to be careful when targeting behavioural changes as they could potentially worsen the epidemic outcome. Furthermore, network structure crucially influences the way that individual-level measures impact the epidemic at the population level. These findings highlight the importance of careful analysis of preventive measures in epidemic models

Bragg Grating Corrosion Sensor

Historically, corrosion has not been included in the calculation of the life expectancy of aircraft. It is well known how stress-corrosion cracking and corrosion fatigue can significantly reduce the life expectancy of structures. Therefore, it can be correctly assumed that some aircraft flying near their expected life might actually be flying well beyond their “safe life”. Furthermore, due to DoD present tight budget requirements, its is expected that some defense aircraft might not be retired at their original expected life but will be reconditioned to fly beyond that time. All of these considerations indicate that early detection, quantification and prevention of corrosion is of critical importance for military aircraft. This is particularly true for Navy aircraft which fly in the most corrosive environment of all services

Multispecies genetic objectives in spatial conservation planning.

The growing threats to biodiversity and global alteration of habitats and species distributions make it increasingly necessary to consider evolutionary patterns in conservation decision-making. Yet there is no clear-cut guidance on how genetic features can be incorporated into conservation planning processes, with multiple molecular markers and several genetic metrics for each marker type to choose from. Genetic patterns also differ between species, but the potential trade-offs amongst genetic objectives for multiple species in conservation planning are currently understudied. This study compares spatial conservation prioritizations derived from two metrics of both genetic diversity (nucleotide and haplotype diversity) and genetic isolation (private haplotypes and local genetic differentiation) for mitochondrial DNA for five marine species. The findings show that conservation plans based solely on habitat representation noticeably differ from those additionally including genetic data, with habitat-based conservation plans selecting fewer conservation priority areas. Furthermore, all four genetic metrics selected approximately similar conservation priority areas, which is likely a result of prioritizing genetic patterns across a genetically diverse array of species. Largely, the results suggest that multi-species genetic conservation objectives are vital to create protected area networks that appropriately preserve community-level evolutionary patterns. This article is protected by copyright. All rights reserved

What happens if you single out? An experiment

We present an experiment investigating the effects of singling out an individual on trust and trustworthiness. We find that (a) trustworthiness falls if there is a singled out subject; (b) non-singled out subjects discriminate against the singled out subject when they are not responsible of the distinct status of this person; (c) under a negative frame, the singled out subject returns significantly less; (d) under a positive frame, the singled out subject behaves bimodally, either selecting very low or very high return rates. Overall, singling out induces a negligible effect on trust but is potentially disruptive for trustworthiness

Traction forces generated during studded boot‐surface interactions on third‐generation artificial turf: A novel mechanistic perspective

The traction forces generated during studded boot–surface interactions affect player performance and injury risk. Over 20 years of empirical research into traction on third generation (3G) artificial turf has met with only limited success in supporting the development of safer surfaces and boots. Thus, the purpose of this perspective article is to present a conceptual framework for generating scientific understanding on 3G turf traction through a novel mechanistic approach. A three-stage framework is proposed. Firstly, the hypothesized traction mechanisms and related analytical equations are identified, namely: friction between the boot outsole and surface; shear resistance of the performance infill layer to the outsole; and compressive resistance of the performance infill layer to horizontal stud displacement. Secondly, a Concept Map is generated to visually represent the contribution of the thirtynine variables identified as directly affecting the traction response. Finally, a Research Roadmap is constructed to guide the direction of future traction studies towards the development of safer surfaces and boots as well as improved mechanical tests to assess surface safety. The proposed framework represents the first attempt to deconstruct bootsurface interactions and hypothesize the science behind the mobilization of traction forces