Homological algebra and friezes

PhD ThesisOver the last decade frieze patterns, as introduced by Conway and Coxeter in the 1970's, have been generalised in many ways. One such exciting development is a homological interpretation of frieze patterns, which we call friezes. A frieze in the modern sense is a map from a triangulated category C to some ring. A frieze X is characterised by the propety that if x ! y ! x is an Auslander-Reiten triangle in C, then X( x)X(x)X(y) = 1. A canonical example of a frieze is the Caldero-Chapoton map. The more general notion of a generalised frieze was introduced by Holm and J rgensen in [25] and [26]. A generalised frieze X0 carries the more general property that X0( x)X0(x) X0(y) 2 f0; 1g. In [25] and [26] Holm and J rgensen also introduced a modi ed Caldero- Chapoton map, which satis es the properties of a generalised frieze. This thesis consists of six chapters. The rst chapter provides a detailed outline of the thesis, whilst setting some of the main results in context and explaining their signi cance. The second chapter provides a necessary background to the notions used throughout the remaining four chapters. We introduce triangulated categories, the derived category, quivers and path algebras, Auslander-Reiten theory and cluster categories, including the polygonal models associated to the cluster categories of Dynkin types An and Dn. The third chapter is based around the proof of a multiplication formula for the modi ed Caldero-Chapoton map, which signi cantly simpli es its computation in practice. We de ne Condition F for two maps and , and show that when our category is 2-Calabi- Yau, Condition F implies that the modi ed Caldero-Chapoton map is a generalised frieze. We then use this to prove our multiplication formula. The de nition of the modi ed Caldero-Chapoton map requires a rigid subcategory R that sits inside a cluster tilting subcategory T. Chapter 4 proves several results showing that in the case of the cluster category of Dynkin type An, the modi ed Caldero-Chapoton map depends only on the rigid subcategory R. These results then allow us to prove a general formula for the group Ksplit 0 (T)=N, which is used in the de nition of the modi ed Caldero-Chapoton map. Chapter 5 provides a comprehensive list of exchange triangles in the cluster category of Dynkin type Dn. Chapter 6 then proves several similar results to Chapter 4 in the case of the cluster category of Dynkin type Dn. We prove that the modi ed Caldero-Chapoton map depends only on the rigid subcategory R before again producing a general formula for Ksplit 0 (T)=

Improvements to the calibration of Electronic Distance Measurement Equipment (EDME)

As Electronic Distance Measurement Equipment (EDME) technology significantly advances, so too must the way instruments are calibrated. Valuable time and resources are committed to ensuring EDME is calibrated to ensure national standards are met. As such, it is vital that the methods employed for calibration are the most appropriate for the instruments used. In order to assist the profession in this regard, this paper investigates the current EDME calibration baseline designs used in Queensland and analyses the suitability of each in order to devise an alternative baseline design. The methodology used was to identify key characteristics of an existing baseline design and select the most accurate of those to construct a new design. This process was then applied over multiple designs and the results analysed and compared to determine the viability of the alternative design

Exploring the educational experiences of young homeless people.

The research explored the educational experiences of young homeless people. It is acknowledged that the outcomes and difficulties experienced within education, are different from those of the homeless population and their housed peers. 7 participants were recruited from Centrepoint, a UK based youth homeless charity, all aged 18-19. Interviews were used to capture the experiences of the young people, and Smith, Flowers & Larkin's IPA stages used to analyse them. Participants’ individual experiences are presented within the research as well as overarching themes found within the participant group. These overarching themes were found to be: 1) needing additional support in school; 2) behavioural or academic failings at school; 3) avoiding failure and building a future; 4) motivation or change in motivation towards education; 5) lack of drive towards education; 6) support from professionals and external organisations; 6) support from teachers; 7) unsupportive educational settings/professionals; 8) challenges meeting basic needs and accessing resources. The findings are discussed within the context of youth homelessness in education, and alongside current research. The research encourages educational professionals to consider how these experiences might impact an individual’s ability to access education, and what school settings can do to support the experience of homeless individuals. Limitations of the research are considered, and opportunities for future research are identified

Is Reducing Uncertain Control the Key to Successful Test Anxiety Intervention for Secondary School Students? Findings From a Randomized Control Trial.

The aim of the study was to conduct a randomized control trial of a targeted, facilitated, test anxiety intervention for a group of adolescent students, and to examine the mediating role of uncertain control. Fifty-six participants (male = 19, white = 21, mean age = 14.7 years) were randomly allocated to an early intervention or wait-list control group. Participants completed the Revised Test Anxiety Scale and the Uncertain Control Scale from the Motivation and Engagement Scale at baseline, after the early intervention group had received the intervention, and again, after the wait-list control group had received the intervention. Participants showed moderate to large reductions in the worry and tension components of test anxiety, and uncertain control, after the intervention. The reduction in worry and tension was partially mediated by the reduction in uncertain control. Findings contribute to the evidence base for test anxiety interventions designed for school age populations and highlight uncertain control as an important factor in test anxiety intervention

Contaminations of soil and two Capsicum annuum generations irrigated by reused urban wastewater treated by different reed beds

Background: In order to save potable water, this study aims to evaluate the contamination of soil and Capsicum annuum L. (chilli) watered with urban wastewater (sewage) pre-treated by various wetland systems. Methods: The appropriateness of wetland outflow for irrigation when applying reused wastewater with high contamination of minerals and pathogens was assessed. The impact of wastewaters pre-treated by various wetlands on soil and harvest was tested in terms of mineral and biological contamination risk. Results: The wetlands met the standards for irrigation water for most water quality variables. However, the thresholds for key water quality parameters were significantly (p < 0.05) exceeded. The highest values for total coliforms, ammonium-nitrogen, phosphorus and potassium were 157,072 CFU/100 mL, 8.5 mg/L, 5.0 mg/L, and 7.0 mg/L, respectively. The harvest was moderately polluted only by zinc according to vegetable quality standards (threshold of 50 mg/kg). Zinc concentrations for Filters 2, 4, 6, 7 and 8 were 35.8, 60.6, 65.1, 65.5 and 53.2 mg/kg, respectively. No bacterial contamination was detected. Conclusions: Treatment of domestic wastewater applying constructed wetlands and subsequent recycling of the treated wastewater for irrigation of crops is a good substitute to the traditional application of drinking water for irrigation purposes

Mangroves enhance the biomass of coral reef fish communities in the Caribbean

Mangrove forests are one of the world's most threatened tropical ecosystems with global loss exceeding 35% (ref. 1). Juvenile coral reef fish often inhabit mangroves, but the importance of these nurseries to reef fish population dynamics has not been quantified. Indeed, mangroves might be expected to have negligible influence on reef fish communities: juvenile fish can inhabit alternative habitats and fish populations may be regulated by other limiting factors such as larval supply or fishing. Here we show that mangroves are unexpectedly important, serving as an intermediate nursery habitat that may increase the survivorship of young fish. Mangroves in the Caribbean strongly influence the community structure of fish on neighbouring coral reefs. In addition, the biomass of several commercially important species is more than doubled when adult habitat is connected to mangroves. The largest herbivorous fish in the Atlantic, Scarus guacamaia, has a functional dependency on mangroves and has suffered local extinction after mangrove removal. Current rates of mangrove deforestation are likely to have severe deleterious consequences for the ecosystem function, fisheries productivity and resilience of reefs. Conservation efforts should protect connected corridors of mangroves, seagrass beds and coral reefs

Measuring the impact of genetic heterogeneity and chromosomal inversions on the efficacy of CRISPR-Cas9 gene drives in different strains of Anopheles gambiae

The human malaria vector Anopheles gambiae is becoming increasingly resistant to insecticides, spurring the development of genetic control strategies. CRISPR-Cas9 gene drives can modify a population by creating double-stranded breaks at highly specific targets, triggering copying of the gene drive into the cut site (‘homing’), ensuring its inheritance. The DNA repair mechanism responsible requires homology between the donor and recipient chromosomes, presenting challenges for the invasion of lab-developed gene drives into wild populations of target species An. gambiae species complex, which show high levels of genome variation. Two gene drives (vas2-5958 and zpg-7280) were introduced into three An. gambiae strains collected across Africa with 5.3-6.6% variation around the target sites, and the effect of this variation on homing was measured. Gene drive homing across different karyotypes of the 2La chromosomal inversion was also assessed. No decrease in gene drive homing was seen despite target site heterology, demonstrating the applicability of gene drives to wild populations

Cryptic population structure and insecticide resistance in Anopheles gambiae from the southern Democratic Republic of Congo

The Democratic Republic of Congo (DRC) suffers from one of the highest malaria burdens worldwide, but information on its Anopheles vector populations is relatively limited. Preventative malaria control in DRC is reliant on pyrethroid-treated nets, raising concerns over the potential impacts of insecticide resistance. We sampled Anopheles gambiae from three geographically distinct populations (Kimpese, Kapolowe and Mikalayi) in southern DRC, collecting from three sub-sites per population and characterising mosquito collections from each for resistance to pyrethroids using WHO tube bioassays. Resistance to each of three different pyrethroids was generally high in An. gambiae with < 92% mortality in all tests, but varied between collections, with mosquitoes from Kimpese being the most resistant. Whole genome sequencing of 165 An. gambiae revealed evidence for genetic differentiation between Kimpese and Kapolowe/Mikalayi, but not between the latter two sample sites despite separation of approximately 800 km. Surprisingly, there was evidence of population structure at a small spatial scale between collection subsites in Kimpese, despite separation of just tens of kilometres. Intra-population (H12) and inter-population (FST) genome scans identified multiple peaks corresponding to genes associated with insecticide resistance such as the voltage gated sodium channel (Vgsc) target site on chromosome 2L, a Cyp6 cytochrome P450 cluster on chromosome arm 2R, and the Cyp9k1 P450 gene on chromosome X. In addition, in the Kimpese subsites, the P450 redox partner gene Cpr showed evidence for contemporary selection (H12) and population differentiation (FST) meriting further exploration as a potential resistance associated marker