Orthogonal polarity graphs and Sidon sets

Determining the maximum number of edges in an $n$-vertex $C_4$-free graph is a well-studied problem that dates back to a paper of Erd\H{o}s from 1938. One of the most important families of $C_4$-free graphs are the Erd\H{o}s-R\'enyi orthogonal polarity graphs. We show that the Cayley sum graph constructed using a Bose-Chowla Sidon set is isomorphic to a large induced subgraph of the Erd\H{o}s-R\'enyi orthogonal polarity graph. Using this isomorphism we prove that the Petersen graph is a subgraph of every sufficiently large Erd\H{o}s-R\'enyi orthogonal polarity graph.Comment: The authors would like to thank Jason Williford for noticing an error in the proof of Theorem 1.2 in the previous version. This error has now been correcte

Junctions podcast

This report outlines the development process for Junctions, an original, mini-drama podcast that explores racial bias in the context of everyday interaction. The report consists of three sections – The Podcast, Pilot Episode, and Future Episodes – each of which speaks to a different aspect of the program’s framework. It also includes nearly all of the planning documents I created during pre-production, production, and post-production.Radio-Television-Fil

Enhancements in reservoir flood risk mapping: example application for Ulley

In July 2007, at Ulley Reservoir, South Yorkshire, a catastrophic dam failure was narrowly avoided due to emergency preventative actions. During the event, a number of homes were evacuated and roads were closed for precautionary measures. Within very close proximity of the reservoir lies the town of Rotherham, the busy M1 motorway and a trunk freight railway line. The incident highlights the need for detailed flood risk and hazard modelling to improve management of the risk and better incident planning.Hazards and population vary in both time and space, but when traditionally modelling flood risk, the population are invariably located within the residential housing stock. This paper innovatively combines flood inundation and spatio-temporal population modelling for better estimates of the population potentially at risk. This is demonstrated though application to Ulley for the most probable worst case failure scenario should the preventative measures not have been undertaken and the dam have failed.This paper proposes an enhanced flood risk assessment in three stages: (i) probabilistic modelling of a failure scenario using embankment breach models; (ii) hydrodynamic inundation modelling for assessment of flood water spreading, depths and velocities; (iii) spatio-temporal population modelling to assess the risk to the population likely to be present. The combination with spatio-temporal population outputs aims to demonstrate the enhancements achievable in reservoir flood risk mapping when vulnerable populations are concerned

Value Creation or Destruction: The Role of Private label in UK Grocery Category Management Decisions

Category management is a collaborative approach between food manufacturers and retailers to manage product categories rather than individual brands. It operates at both strategic and operational levels and seeks to create value ultimately for the consumer. The paper contributes to the literature and practice. It uses a qualitative interview study of twenty five senior practitioners and explores the role of private label products within UK grocery categories as consumers continue to switch due to lower prices and comparable quality to the traditional brands. The research also examines how private label manufacturers can create value within the category management relationship and how they can aspire to category captainship if they generate retailer specific and differentiated category strategies. The paper accepts its limitations and explains how further research in this important field of retailing is necessary to update the literature and help practitioners navigate their way through turbulent sector change

Characterization of quantum well structures using a photocathode electron microscope

Present day integrated circuits pose a challenge to conventional electronic and mechanical test methods. Feature sizes in the submicron and nanometric regime require radical approaches in order to facilitate electrical contact to circuits and devices being tested. In addition, microwave operating frequencies require careful attention to distributed effects when considering the electrical signal paths within and external to the device under test. An alternative testing approach which combines the best of electrical and optical time domain testing is presented, namely photocathode electron microscope quantitative voltage contrast (PEMQVC)