The meet property in local degree structures

In this thesis we look at whether two different classes of local Turing degrees (the c.e. degrees, and the 1-generic degrees below 0') satisfy the meet property - where a degree a satisfies the meet property if it is incomputable and for all b < a there exists a non-zero degree c such that a ∧ c = 0. We first give a general discussion of the Turing Degrees and certain known results, before giving a brief introduction to priority arguments. This is followed by some more technical considerations (full approximation and minimal degree constructions) before the proof of two new theorems - the first concerning c.e. degrees and the meet property and the second concerning 1 − generic degrees and the meet property. Chapter 1 contains a broad introduction to the Turing Degrees, and Chapter 2 to the Local Degrees. In Chapter 3 we consider minimal degree constructions, which we use in Chapter 4 to prove our first new theorem - Theorem 4.2.1 Given any non-zero c.e. degree a and any degree b < a, there is a minimal degree m < a such that m ≰ b. From which we get Corollary 4.2.2 Every c.e. degree satisfies the meet property - answering a question first asked by Cooper and Epstein in the 1980s. In Chapter 5 we prove the second new theorem - Theorem 5.2.2 There exists a 1 − generic degree which does not satisfy the meet property - showing that a result from Kumabe in the 1990s does not extend to the case n = 1

Computably enumerable Turing degrees and the meet property

Working in the Turing degree structure, we show that those degrees which contain computably enumerable sets all satisfy the meet property, i.e. if a is c.e. and b < a, then there exists non-zero m < a with b ^m = 0. In fact, more than this is true: m may always be chosen to be a minimal degree. This settles a conjecture of Cooper and Epstein from the 80s

Overnight consolidation aids the transfer of statistical knowledge from the medial temporal lobe to the striatum

Sleep is important for abstraction of the underlying principles (or gist) which bind together conceptually related stimuli, but little is known about the neural correlates of this process. Here, we investigate this issue using overnight sleep monitoring and functional magnetic resonance imaging (fMRI). Participants were exposed to a statistically structured sequence of auditory tones then tested immediately for recognition of short sequences which conformed to the learned statistical pattern. Subsequently, after consolidation over either 30min or 24h, they performed a delayed test session in which brain activity was monitored with fMRI. Behaviorally, there was greater improvement across 24h than across 30min, and this was predicted by the amount of slow wave sleep (SWS) obtained. Functionally, we observed weaker parahippocampal responses and stronger striatal responses after sleep. Like the behavioral result, these differences in functional response were predicted by the amount of SWS obtained. Furthermore, connectivity between striatum and parahippocampus was weaker after sleep, whereas connectivity between putamen and planum temporale was stronger. Taken together, these findings suggest that abstraction is associated with a gradual shift from the hippocampal to the striatal memory system and that this may be mediated by SWS

Children in care: Where do children entering care at different ages end up? An analysis of local authority administrative data

Local authorities in England are required to routinely collect administrative data on children in care and cross-sectional analyses of national data are published by central government. This paper explores the usefulness of undertaking a longitudinal analysis of these data at local authority level to determine the care pathways for children entering care, differentiating by age at entry. The sample consisted of 2208 children who entered care in one English local authority over a six-year period, and who were followed up for at least 2 years. A logistic regression model was fitted to explore factors associated with children staying long term in care. Age at entry was a key determinant of where children ended up (return to a parent, special guardianship or residence order, adoption or staying long term in care). Only a minority of entrants (mainly those entering care in their middle years) remained in longer term care. For the vast majority of children, the ‘pre-care family context’ remains important as children will either return to parents or relatives or stay in touch with them. The findings are used to urge service planners to make full use of data on care entrants, especially age at entry, when deciding on the balance between the different placement options needed, and the social work service delivery models

Roadmap on Photovoltaic Absorber Materials for Sustainable Energy Conversion

Photovoltaics (PVs) are a critical technology for curbing growing levels of anthropogenic greenhouse gas emissions, and meeting increases in future demand for low-carbon electricity. In order to fulfil ambitions for net-zero carbon dioxide equivalent (CO2eq) emissions worldwide, the global cumulative capacity of solar PVs must increase by an order of magnitude from 0.9 TWp in 2021 to 8.5 TWp by 2050 according to the International Renewable Energy Agency, which is considered to be a highly conservative estimate. In 2020, the Henry Royce Institute brought together the UK PV community to discuss the critical technological and infrastructure challenges that need to be overcome to address the vast challenges in accelerating PV deployment. Herein, we examine the key developments in the global community, especially the progress made in the field since this earlier roadmap, bringing together experts primarily from the UK across the breadth of the photovoltaics community. The focus is both on the challenges in improving the efficiency, stability and levelized cost of electricity of current technologies for utility-scale PVs, as well as the fundamental questions in novel technologies that can have a significant impact on emerging markets, such as indoor PVs, space PVs, and agrivoltaics. We discuss challenges in advanced metrology and computational tools, as well as the growing synergies between PVs and solar fuels, and offer a perspective on the environmental sustainability of the PV industry. Through this roadmap, we emphasize promising pathways forward in both the short- and long-term, and for communities working on technologies across a range of maturity levels to learn from each other.Comment: 160 pages, 21 figure

Sixteen diverse laboratory mouse reference genomes define strain-specific haplotypes and novel functional loci.

We report full-length draft de novo genome assemblies for 16 widely used inbred mouse strains and find extensive strain-specific haplotype variation. We identify and characterize 2,567 regions on the current mouse reference genome exhibiting the greatest sequence diversity. These regions are enriched for genes involved in pathogen defence and immunity and exhibit enrichment of transposable elements and signatures of recent retrotransposition events. Combinations of alleles and genes unique to an individual strain are commonly observed at these loci, reflecting distinct strain phenotypes. We used these genomes to improve the mouse reference genome, resulting in the completion of 10 new gene structures. Also, 62 new coding loci were added to the reference genome annotation. These genomes identified a large, previously unannotated, gene (Efcab3-like) encoding 5,874 amino acids. Mutant Efcab3-like mice display anomalies in multiple brain regions, suggesting a possible role for this gene in the regulation of brain development