Computing data for Levin-Wen with defects

We demonstrate how to do many computations for non-chiral topological phases with defects. These defects may be 1-dimensional domain walls or 0-dimensional point defects. Using $\operatorname{Vec}(S_3)$ as a guiding example, we demonstrate how domain wall fusion and associators can be computed using generalized tube algebra techniques. These domain walls can be both between distinct or identical phases. Additionally, we show how to compute all possible point defects, and the fusion and associator data of these. Worked examples, tabulated data and Mathematica code are provided.Comment: 17+25 pages, many tables and attached cod

Fusing Binary Interface Defects in Topological Phases: The Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z}) case

A binary interface defect is any interface between two (not necessarily invertible) domain walls. We compute all possible binary interface defects in Kitaev's $\mathbb{Z}/p\mathbb{Z}$ model and all possible fusions between them. Our methods can be applied to any Levin-Wen model. We also give physical interpretations for each of the defects in the $\mathbb{Z}/p\mathbb{Z}$ model. These physical interpretations provide a new graphical calculus which can be used to compute defect fusion.Comment: 27+10 pages, 2+5 tables, comments welcom

Calculating pp-values and their significances with the Energy Test for large datasets

The energy test method is a multi-dimensional test of whether two samples are consistent with arising from the same underlying population, through the calculation of a single test statistic (called the $T$-value). The method has recently been used in particle physics to search for differences between samples that arise from CP violation. The generalised extreme value function has previously been used to describe the distribution of $T$-values under the null hypothesis that the two samples are drawn from the same underlying population. We show that, in a simple test case, the distribution is not sufficiently well described by the generalised extreme value function. We present a new method, where the distribution of $T$-values under the null hypothesis when comparing two large samples can be found by scaling the distribution found when comparing small samples drawn from the same population. This method can then be used to quickly calculate the $p$-values associated with the results of the test.Comment: 9 pages (including title page); 4 figure

Computing Defects Associated to Bounded Domain Wall Structures: The Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z}) Case

A domain wall structure consists of a planar graph with faces labeled by fusion categories/topological phases. Edges are labeled by bimodules/domain walls. When the vertices are labeled by point defects we get a compound defect. We present an algorithm, called the domain wall structure algorithm, for computing the compound defect. We apply this algorithm to show that the \emph{bimodule associator}, related to the $O_3$ obstruction of [Etingof et al., Quantum Topol. 1, 209 (2010), arXiv:0909.3140], is trivial for all domain walls of $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$. In the language of this paper, the ground states of the Levin-Wen model are compound defects. We use this to define a generalization of the Levin-Wen model with domain walls and point defects. The domain wall structure algorithm can be used to compute the ground states of these generalized Levin-Wen type models.Comment: 16+10 pages, 7 tables, comments welcom

Domain walls in topological phases and the Brauer-Picard ring for Vec⁡(Z/pZ)\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})

We show how to calculate the relative tensor product of bimodule categories (not necessarily invertible) using ladder string diagrams. As an illustrative example, we compute the Brauer-Picard ring for the fusion category $\operatorname{Vec}(\mathbb{Z}/p\mathbb{Z})$. Moreover, we provide a physical interpretation of all indecomposable bimodule categories in terms of domain walls in the associated topological phase. We show how this interpretation can be used to compute the Brauer-Picard ring from a physical perspective.Comment: 16 pages, 1 figure, 3 tables, comments welcom

Influence of anodizing process on fatigue life of a machined aluminium alloy

In order to investigate the coupled effects of machining and anodizing processes on fatigue life of alloy 7010-T7451, a series of rotating bending fatigue tests were conducted at 60Hz. In the as machined condition, test results showed that fatigue life is surface roughness dependent and that fatigue life decreases with an increase in surface roughness and this effect is found to be more pronounced in high cycle fatigue where major portion of fatigue life is consumed in nucleating the cracks. Effects of pretreatments, like degreasing and pickling employed prior to anodizing, on fatigue life of the given alloy were also studied. Results demonstrated that degreasing showed no change in fatigue life while pickling had negative impact on fatigue life of specimens. The small decrease in fatigue life of anodized specimens as compare to pickled specimens is attributed to brittle and microcracking of the coating. Scanning electron microscopic (SEM) examination revealed multi-site crack initiation for the pickled and anodized specimens. SEM examination showed that pickling solution attacked the grain boundaries and intermetallic inclusions present on the surface resulting in pits formation. These pits are of primary concern with respect to accelerated fatigue crack nucleation and subsequent anodized coating formation

The Change Up Project : using social norming theory with young people to address domestic abuse and promote healthy relationships

This paper presents the findings of a secondary analysis of data collected during a pilot project, Change Up, which used a social norming approach (SNA) to address domestic violence and abuse (DVA) with young people aged 13–14. A SNA is based upon a well-articulated theory of behavior and evidence-based methodology for addressing social justice issues. This reflects a paradigm shift focusing upon strengths and positives, rather than pathologizing behaviours. Adopting a SNA, the Change Up project comprised a baseline survey followed by the intervention (workshop and peer-to-peer campaign), ending with a post-intervention survey. It was delivered in two high schools in a UK city between 2015 and 16. A secondary analysis of the survey data collected during the surveys and qualitative data collected at the end of each workshop was undertaken and this is reported here. Change Up data illustrates that most young people in the sample thought that DVA is unacceptable. There was, however, a gender difference in the norms held about the social acceptability of girls using physical violence against boys (and vice versa). The analysis of Change Up data indicates that a social norming approach to DVA programs aimed at young people can be successful in promoting attitude and behaviour change. It also highlights a continuing need for young people’s education about relationships and gender equality

Photonic Quantum Logic with Narrowband Light from Single Atoms

Increasing control of single photons enables new applications of photonic quantum-enhanced technology and further experimental exploration of fundamental quantum phenomena. Here, we demonstrate quantum logic using narrow linewidth photons that are produced under nearly perfect quantum control from a single ^87Rb atom strongly coupled to a high-finesse cavity. We use a controlled- NOT gate integrated into a photonic chip to entangle these photons, and we observe non-classical correlations between events separated by periods exceeding the travel time across the chip by three orders of magnitude. This enables quantum technology that will use the properties of both narrowband single photon sources and integrated quantum photonics, such as networked quantum computing, narrow linewidth quantum enhanced sensing and atomic memories.Comment: 5 pates, 3 figure

Pornography, sexual coercion and abuse and sexting in young people’s intimate relationships: A European study

New technology has made pornography increasingly accessible to young people, and a growing evidence base has identified a relationship between viewing pornography and violent or abusive behavior in young men. This article reports findings from a large survey of 4,564 young people aged 14 to 17 in five European countries which illuminate the relationship between regular viewing of online pornography, sexual coercion and abuse and the sending and receiving of sexual images and messages, known as “sexting.” In addition to the survey, which was completed in schools, 91 interviews were undertaken with young people who had direct experience of interpersonal violence and abuse in their own relationships. Rates for regularly viewing online pornography were very much higher among boys and most had chosen to watch pornography. Boys’ perpetration of sexual coercion and abuse was significantly associated with regular viewing of online pornography. Viewing online pornography was also associated with a significantly increased probability of having sent sexual images/messages for boys in nearly all countries. In addition, boys who regularly watched online pornography were significantly more likely to hold negative gender attitudes. The qualitative interviews illustrated that, although sexting is normalized and perceived positively by most young people, it has the potential to reproduce sexist features of pornography such as control and humiliation. Sex and relationships education should aim to promote a critical understanding of pornography among young people that recognizes its abusive and gendered values