An existence theorem for solutions to a model problem with Yamabe-positive metric for conformal parameterizations of the Einstein constraint equations

Thesis (M.S.) University of Alaska Fairbanks, 2016We use the conformal method to investigate solutions of the vacuum Einstein constraint equations on a manifold with a Yamabe-positive metric. To do so, we develop a model problem with symmetric data on Sn⁻¹ x S¹. We specialize the model problem to a two-parameter family of conformal data, and find that no solutions exist when the transverse-traceless tensor is identically zero. When the transverse traceless tensor is nonzero, we observe an existence theorem in both the near-constant mean curvature and far-from-constant mean curvature regimes.Chapter 1: Introduction and Background -- 1.1 Motivation -- 1.2 Overview of Relativity -- 1.3 Geometric Formulation of General Relativity -- 1.4 The Constraint Equations -- 1.5 Conformal Parameterizations -- Chapter 2: Symmetric Data on Sn⁻¹ x S¹ -- Chapter 3: Solutions of the Constraint Equations -- 3.1. Summary of Results -- 3.2. Reduction to Root Finding -- 3.3. Solutions of F(b) = 1 -- 3.3.1. Elementary Estimates for F -- 3.3.2 Proof of Theorem 1 (Near-CMC Results) -- 3.3.3 Proof of Theorem 2 (Existence) -- Chapter 4: Conclusion and Future Work -- References

Numerical Analysis and Gravity

In this dissertation we apply techniques of numerical analysis to current questions related to understanding gravity. The first question is that of sources of gravitational waves: how can we accurately determine the intrinsic physical parameters of a binary system whose late inspiral and merger was detected by the Laser Interferometer Gravitational-Wave Observatory. In particular, state-of-the-art algorithms for producing theoretical waveforms are as many as three orders of magnitude too slow for timely analysis. We show that direct software optimization produces a two order of magnitude speedup. We also describe documentation efforts undertaken so that the software may be rewritten to enhance both performance and physical realism. The second question is that of measuring Newton\u27s gravitational constant G. In particular, the results of experiments measuring G have differed by as many as ten standard deviations. Measuring the oscillation frequency of a magnetically-levitated microsphere shows promise for sharpening the value of G, and the system for this measurement was found to accurately measure low-frequency accelerations. As such, this system forms a prototype for a room-temperature, low-mass accelerometer. At the center of the accelerometer and G measurements lies a new image analysis technique we developed for determining the position of the microsphere to 1.6 nm

Understanding acute ankle ligamentous sprain injury in sports

This paper summarizes the current understanding on acute ankle sprain injury, which is the most common acute sport trauma, accounting for about 14% of all sport-related injuries. Among, 80% are ligamentous sprains caused by explosive inversion or supination. The injury motion often happens at the subtalar joint and tears the anterior talofibular ligament (ATFL) which possesses the lowest ultimate load among the lateral ligaments at the ankle. For extrinsic risk factors to ankle sprain injury, prescribing orthosis decreases the risk while increased exercise intensity in soccer raises the risk. For intrinsic factors, a foot size with increased width, an increased ankle eversion to inversion strength, plantarflexion strength and ratio between dorsiflexion and plantarflexion strength, and limb dominance could increase the ankle sprain injury risk. Players with a previous sprain history, players wearing shoes with air cells, players who do not stretch before exercising, players with inferior single leg balance, and overweight players are 4.9, 4.3, 2.6, 2.4 and 3.9 times more likely to sustain an ankle sprain injury. The aetiology of most ankle sprain injuries is incorrect foot positioning at landing – a medially-deviated vertical ground reaction force causes an explosive supination or inversion moment at the subtalar joint in a short time (about 50 ms). Another aetiology is the delayed reaction time of the peroneal muscles at the lateral aspect of the ankle (60–90 ms). The failure supination or inversion torque is about 41–45 Nm to cause ligamentous rupture in simulated spraining tests on cadaver. A previous case report revealed that the ankle joint reached 48 degrees inversion and 10 degrees internal rotation during an accidental grade I ankle ligamentous sprain injury during a dynamic cutting trial in laboratory. Diagnosis techniques and grading systems vary, but the management of ankle ligamentous sprain injury is mainly conservative. Immobilization should not be used as it results in joint stiffness, muscle atrophy and loss of proprioception. Traditional Chinese medicine such as herbs, massage and acupuncture were well applied in China in managing sports injuries, and was reported to be effective in relieving pain, reducing swelling and edema, and restoring normal ankle function. Finally, the best practice of sports medicine would be to prevent the injury. Different previous approaches, including designing prophylactice devices, introducing functional interventions, as well as change of games rules were highlighted. This paper allows the readers to catch up with the previous researches on ankle sprain injury, and facilitate the future research idea on sport-related ankle sprain injury

Whole-genome sequencing reveals host factors underlying critical COVID-19

Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care1 or hospitalization2–4 after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes—including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)—in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease

The paradoxical role of meritocratic selection in the perpetuation of social inequalities at school

The school system is intended to offer all students the same opportunities, but most international surveys reveal an overall lower achievement for students from disadvantaged groups compared with more advantaged students. Recent experimental research in social psychology has demonstrated that schools as institutions contribute with their implicit cultural norms and structure to the production of inequalities. This chapter examines the role that a structural feature of school, namely meritocratic selection, plays in this reproduction of inequalities at school. First, we describe how meritocracy in the educational system can hold paradoxical effects by masking the virtuous/vicious cycles of opportunities created by educational institutions. Second, we present recent research suggesting that selection practices relying on a meritocratic principle—more than other practices—can lead to biased academic decisions hindering disadvantaged students. We propose that inequalities in school might not just result from isolated failures in an otherwise functional meritocratic system, but rather that merit-based selection itself contributes to the perpetuation of inequalities at school