Numerical Algorithms for finding Black Hole solutions of Einstein's Equations

Einstein's Theory of General Relativity has proven remarkably successful at modelling a wide range of gravitational phenomena. Amongst some of the novel features in this description is the existence of black holes; regions of space-time where gravity is so strong that light cannot escape. The properties of black holes have been extensively studied within General Relativity, culminating in the result that the few known space-times are the only allowed stationary black hole solutions in four dimensions. In the past half century, research has focused on how to unify the distinct theories of gravity and quantum mechanics. A common theme amongst several strong candidates is that space-time, the backdrop for gravity, is fundamentally higher dimensional. In these theories, the structure of black hole solutions is relatively unknown and expected to be much richer; finding such solutions is, however, a very hard task. In this thesis, we introduce new numerical methods to study higher dimensional black holes. The methods, based on refinements of existing work and the novel application of standard techniques, are then used to study a number of black hole space-times. Namely the structure of black holes on a Kaluza-Klein background, and rotating Kerr black holes. We demonstrate that these algorithms can be applied in a wide class of situations and yield good quality results with comparative ease. New results are presented in both cases studied. We examine the predicted merger between non-uniform black strings and localised black holes on a Kaluza-Klein background. We find evidence for a new type of non-uniform black string with one Euclidean negative mode and lower entropy than the uniform strings. We discover a window of localised black holes with one Euclidean negative mode but positive specific heat. We also look at the local structure of the merger point and find consistency with Kol's cone prediction

The Effects of a Natural Polyphenol Extract from Sugarcane (Saccharum officinarum) on the Growth, Survival, and Feed Conversion Efficiency of Juvenile Black Tiger Shrimp (Penaeus monodon)

Farmed shrimp feeds are under continuous development to maximise shrimp growth, health, and feed efficiency. There is evidence in aquaculture species that botanical ingredients may be capable of improvements in each of these traits. However, the full potential of these ingredients remains largely unexplored. We investigated the effect of dietary additions of a polyphenol-rich sugarcane extract (PRSE) at the rate of 0, 2, 4, or 6 g kg−1 of diet, on the growth, survival, feed conversion ratio, and pathogen loading of black tiger shrimp (Penaeus monodon) over a 10-week feeding period in a small-scale intensive RAS system. Shrimp fed the highest level of PRSE compared to the control were 54% heavier (15.4 vs. 10.0 g; p 0.05). These findings demonstrate that polyphenol-rich sugarcane extracts have the potential to improve shrimp growth and FCR when added into feed formulations. Further research should be conducted in commercial rearing conditions for validation

Innovations, challenges, and minimal information for standardization of humanized mice.

Mice xenotransplanted with human cells and/or expressing human gene products (also known as "humanized mice") recapitulate the human evolutionary specialization and diversity of genotypic and phenotypic traits. These models can provide a relevant in vivo context for understanding of human-specific physiology and pathologies. Humanized mice have advanced toward mainstream preclinical models and are now at the forefront of biomedical research. Here, we considered innovations and challenges regarding the reconstitution of human immunity and human tissues, modeling of human infections and cancer, and the use of humanized mice for testing drugs or regenerative therapy products. As the number of publications exploring different facets of humanized mouse models has steadily increased in past years, it is becoming evident that standardized reporting is needed in the field. Therefore, an international community-driven resource called "Minimal Information for Standardization of Humanized Mice" (MISHUM) has been created for the purpose of enhancing rigor and reproducibility of studies in the field. Within MISHUM, we propose comprehensive guidelines for reporting critical information generated using humanized mice

A numerical approach to finding general stationary vacuum black holes

The Harmonic Einstein equation is the vacuum Einstein equation supplemented by a gauge fixing term which we take to be that of DeTurck. For static black holes analytically continued to Riemannian manifolds without boundary at the horizon this equation has previously been shown to be elliptic, and Ricci flow and Newton's method provide good numerical algorithms to solve it. Here we extend these techniques to the arbitrary cohomogeneity stationary case which must be treated in Lorentzian signature. For stationary spacetimes with globally timelike Killing vector the Harmonic Einstein equation is elliptic. In the presence of horizons and ergo-regions it is less obviously so. Motivated by the Rigidity theorem we study a class of stationary black hole spacetimes, considered previously by Harmark, general enough to include the asymptotically flat case in higher dimensions. We argue the Harmonic Einstein equation consistently truncates to this class of spacetimes giving an elliptic problem. The Killing horizons and axes of rotational symmetry are boundaries for this problem and we determine boundary conditions there. As a simple example we numerically construct 4D rotating black holes in a cavity using Anderson's boundary conditions. We demonstrate both Newton's method and Ricci flow to find these Lorentzian solutions.Comment: 43 pages, 7 figure

Proceedings of Patient Reported Outcome Measure’s (PROMs) Conference Oxford 2017: Advances in Patient Reported Outcomes Research

A33-Effects of Out-of-Pocket (OOP) Payments and Financial Distress on Quality of Life (QoL) of People with Parkinson’s (PwP) and their Carer

Evaluating the Effects of SARS-CoV-2 Spike Mutation D614G on Transmissibility and Pathogenicity.

Global dispersal and increasing frequency of the SARS-CoV-2 spike protein variant D614G are suggestive of a selective advantage but may also be due to a random founder effect. We investigate the hypothesis for positive selection of spike D614G in the United Kingdom using more than 25,000 whole genome SARS-CoV-2 sequences. Despite the availability of a large dataset, well represented by both spike 614 variants, not all approaches showed a conclusive signal of positive selection. Population genetic analysis indicates that 614G increases in frequency relative to 614D in a manner consistent with a selective advantage. We do not find any indication that patients infected with the spike 614G variant have higher COVID-19 mortality or clinical severity, but 614G is associated with higher viral load and younger age of patients. Significant differences in growth and size of 614G phylogenetic clusters indicate a need for continued study of this variant

SARS-CoV-2 Omicron is an immune escape variant with an altered cell entry pathway

Vaccines based on the spike protein of SARS-CoV-2 are a cornerstone of the public health response to COVID-19. The emergence of hypermutated, increasingly transmissible variants of concern (VOCs) threaten this strategy. Omicron (B.1.1.529), the fifth VOC to be described, harbours multiple amino acid mutations in spike, half of which lie within the receptor-binding domain. Here we demonstrate substantial evasion of neutralization by Omicron BA.1 and BA.2 variants in vitro using sera from individuals vaccinated with ChAdOx1, BNT162b2 and mRNA-1273. These data were mirrored by a substantial reduction in real-world vaccine effectiveness that was partially restored by booster vaccination. The Omicron variants BA.1 and BA.2 did not induce cell syncytia in vitro and favoured a TMPRSS2-independent endosomal entry pathway, these phenotypes mapping to distinct regions of the spike protein. Impaired cell fusion was determined by the receptor-binding domain, while endosomal entry mapped to the S2 domain. Such marked changes in antigenicity and replicative biology may underlie the rapid global spread and altered pathogenicity of the Omicron variant

Evaluating the Effects of SARS-CoV-2 Spike Mutation D614G on Transmissibility and Pathogenicity

Global dispersal and increasing frequency of the SARS-CoV-2 spike protein variant D614G are suggestive of a selective advantage but may also be due to a random founder effect. We investigate the hypothesis for positive selection of spike D614G in the United Kingdom using more than 25,000 whole genome SARS-CoV-2 sequences. Despite the availability of a large dataset, well represented by both spike 614 variants, not all approaches showed a conclusive signal of positive selection. Population genetic analysis indicates that 614G increases in frequency relative to 614D in a manner consistent with a selective advantage. We do not find any indication that patients infected with the spike 614G variant have higher COVID-19 mortality or clinical severity, but 614G is associated with higher viral load and younger age of patients. Significant differences in growth and size of 614G phylogenetic clusters indicate a need for continued study of this variant

Hospital admission and emergency care attendance risk for SARS-CoV-2 delta (B.1.617.2) compared with alpha (B.1.1.7) variants of concern: a cohort study

Background: The SARS-CoV-2 delta (B.1.617.2) variant was first detected in England in March, 2021. It has since rapidly become the predominant lineage, owing to high transmissibility. It is suspected that the delta variant is associated with more severe disease than the previously dominant alpha (B.1.1.7) variant. We aimed to characterise the severity of the delta variant compared with the alpha variant by determining the relative risk of hospital attendance outcomes. Methods: This cohort study was done among all patients with COVID-19 in England between March 29 and May 23, 2021, who were identified as being infected with either the alpha or delta SARS-CoV-2 variant through whole-genome sequencing. Individual-level data on these patients were linked to routine health-care datasets on vaccination, emergency care attendance, hospital admission, and mortality (data from Public Health England's Second Generation Surveillance System and COVID-19-associated deaths dataset; the National Immunisation Management System; and NHS Digital Secondary Uses Services and Emergency Care Data Set). The risk for hospital admission and emergency care attendance were compared between patients with sequencing-confirmed delta and alpha variants for the whole cohort and by vaccination status subgroups. Stratified Cox regression was used to adjust for age, sex, ethnicity, deprivation, recent international travel, area of residence, calendar week, and vaccination status. Findings: Individual-level data on 43 338 COVID-19-positive patients (8682 with the delta variant, 34 656 with the alpha variant; median age 31 years [IQR 17–43]) were included in our analysis. 196 (2·3%) patients with the delta variant versus 764 (2·2%) patients with the alpha variant were admitted to hospital within 14 days after the specimen was taken (adjusted hazard ratio [HR] 2·26 [95% CI 1·32–3·89]). 498 (5·7%) patients with the delta variant versus 1448 (4·2%) patients with the alpha variant were admitted to hospital or attended emergency care within 14 days (adjusted HR 1·45 [1·08–1·95]). Most patients were unvaccinated (32 078 [74·0%] across both groups). The HRs for vaccinated patients with the delta variant versus the alpha variant (adjusted HR for hospital admission 1·94 [95% CI 0·47–8·05] and for hospital admission or emergency care attendance 1·58 [0·69–3·61]) were similar to the HRs for unvaccinated patients (2·32 [1·29–4·16] and 1·43 [1·04–1·97]; p=0·82 for both) but the precision for the vaccinated subgroup was low. Interpretation: This large national study found a higher hospital admission or emergency care attendance risk for patients with COVID-19 infected with the delta variant compared with the alpha variant. Results suggest that outbreaks of the delta variant in unvaccinated populations might lead to a greater burden on health-care services than the alpha variant. Funding: Medical Research Council; UK Research and Innovation; Department of Health and Social Care; and National Institute for Health Research

Changes in symptomatology, reinfection, and transmissibility associated with the SARS-CoV-2 variant B.1.1.7: an ecological study

Background The SARS-CoV-2 variant B.1.1.7 was first identified in December, 2020, in England. We aimed to investigate whether increases in the proportion of infections with this variant are associated with differences in symptoms or disease course, reinfection rates, or transmissibility. Methods We did an ecological study to examine the association between the regional proportion of infections with the SARS-CoV-2 B.1.1.7 variant and reported symptoms, disease course, rates of reinfection, and transmissibility. Data on types and duration of symptoms were obtained from longitudinal reports from users of the COVID Symptom Study app who reported a positive test for COVID-19 between Sept 28 and Dec 27, 2020 (during which the prevalence of B.1.1.7 increased most notably in parts of the UK). From this dataset, we also estimated the frequency of possible reinfection, defined as the presence of two reported positive tests separated by more than 90 days with a period of reporting no symptoms for more than 7 days before the second positive test. The proportion of SARS-CoV-2 infections with the B.1.1.7 variant across the UK was estimated with use of genomic data from the COVID-19 Genomics UK Consortium and data from Public Health England on spike-gene target failure (a non-specific indicator of the B.1.1.7 variant) in community cases in England. We used linear regression to examine the association between reported symptoms and proportion of B.1.1.7. We assessed the Spearman correlation between the proportion of B.1.1.7 cases and number of reinfections over time, and between the number of positive tests and reinfections. We estimated incidence for B.1.1.7 and previous variants, and compared the effective reproduction number, Rt, for the two incidence estimates. Findings From Sept 28 to Dec 27, 2020, positive COVID-19 tests were reported by 36 920 COVID Symptom Study app users whose region was known and who reported as healthy on app sign-up. We found no changes in reported symptoms or disease duration associated with B.1.1.7. For the same period, possible reinfections were identified in 249 (0·7% [95% CI 0·6–0·8]) of 36 509 app users who reported a positive swab test before Oct 1, 2020, but there was no evidence that the frequency of reinfections was higher for the B.1.1.7 variant than for pre-existing variants. Reinfection occurrences were more positively correlated with the overall regional rise in cases (Spearman correlation 0·56–0·69 for South East, London, and East of England) than with the regional increase in the proportion of infections with the B.1.1.7 variant (Spearman correlation 0·38–0·56 in the same regions), suggesting B.1.1.7 does not substantially alter the risk of reinfection. We found a multiplicative increase in the Rt of B.1.1.7 by a factor of 1·35 (95% CI 1·02–1·69) relative to pre-existing variants. However, Rt fell below 1 during regional and national lockdowns, even in regions with high proportions of infections with the B.1.1.7 variant. Interpretation The lack of change in symptoms identified in this study indicates that existing testing and surveillance infrastructure do not need to change specifically for the B.1.1.7 variant. In addition, given that there was no apparent increase in the reinfection rate, vaccines are likely to remain effective against the B.1.1.7 variant. Funding Zoe Global, Department of Health (UK), Wellcome Trust, Engineering and Physical Sciences Research Council (UK), National Institute for Health Research (UK), Medical Research Council (UK), Alzheimer's Society