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

Cross-correlation image analysis for real-time particle tracking

Accurately measuring translations between images is essential in many fields, including biology, medicine, geography, and physics. Existing methods, including the popular FFT-based cross-correlation, are not suitable for real-time analysis, which is especially vital in feedback control systems. To fill this gap, we introduce a new algorithm which approaches shot-noise limited displacement detection and a GPU-based implementation for real-time image analysis.Comment: 4 pages, 3 figures, submitted to Optics Letter

Empirical Research into White Racialized Identities in Britain

The intellectual project of using whiteness as an explicit tool of analysis is not one that has taken root in Britain. However, there are a number of empirical studies that investigate the racialization of white identities. In this article, I look at some empirical sociological fieldwork carried out on white identities in Britain since the early 1990s and identify the key themes arising. These themes are (in)visibility, norms and values, cultural capital and integration, contingent hierarchies and Empire in the present. In Britain, a pertinent distinction is between rural and urban settings for the enactment of white identities vis-a`-vis those of minorities, and there is an exploration of some of the contingency that draws the boundary between ‘white’ and ‘Other’ in different places. Areas of commonality and distinctiveness are noted in terms of the American work. In the last section, I argue that there are a number of issues to resolve around continuing such studies, including linking the micro-level to the macro-level analysis, and expanding to international comparative work

Genetic influences on externalizing psychopathology overlap with cognitive functioning and show developmental variation

Background: Questions remain regarding whether genetic influences on early life psychopathology overlap with cognition and show developmental variation. Methods: Using data from 9,421 individuals aged 8-21 from the Philadelphia Neurodevelopmental Cohort, factors of psychopathology were generated using a bifactor model of item-level data from a psychiatric interview. Five orthogonal factors were generated: anxious-misery (mood and anxiety), externalizing (attention deficit hyperactivity and conduct disorder), fear (phobias), psychosis-spectrum, and a general factor. Genetic analyses were conducted on a subsample of 4,662 individuals of European American ancestry. A genetic relatedness matrix was used to estimate heritability of these factors, and genetic correlations with executive function, episodic memory, complex reasoning, social cognition, motor speed, and general cognitive ability. Gene × Age analyses determined whether genetic influences on these factors show developmental variation. Results: Externalizing was heritable (h2 = 0.46, p = 1 × 10-6), but not anxious-misery (h2 = 0.09, p = 0.183), fear (h2 = 0.04, p = 0.337), psychosis-spectrum (h2 = 0.00, p = 0.494), or general psychopathology (h2 = 0.21, p = 0.040). Externalizing showed genetic overlap with face memory (ρg = -0.412, p = 0.004), verbal reasoning (ρg = -0.485, p = 0.001), spatial reasoning (ρg = -0.426, p = 0.010), motor speed (ρg = 0.659, p = 1x10-4), verbal knowledge (ρg = -0.314, p = 0.002), and general cognitive ability (g)(ρg = -0.394, p = 0.002). Gene × Age analyses revealed decreasing genetic variance (γg = -0.146, p = 0.004) and increasing environmental variance (γe = 0.059, p = 0.009) on externalizing. Conclusions: Cognitive impairment may be a useful endophenotype of externalizing psychopathology and, therefore, help elucidate its pathophysiological underpinnings. Decreasing genetic variance suggests that gene discovery efforts may be more fruitful in children than adolescents or young adults