Thesis (Ph. D.)--University of Michigan, 1934. / Lithoprinted. "Reprinted from the Annals of Mathematical Statistics, November, 1933."

Thesis (Ph. D.)--University of Chicago, 1933. / Vita. Lithoprinted. "Private edition, distributed by the University of Chicago libraries, Chicago, Illinois."

Thesis--M.A., University of Hong Kong. / Typescript.

Using pencils of quadrics, we study a construction of torsors of Jacobians of hyperelliptic curves twice of which is Pic^1. We then use this construction to study the arithmetic invariant theory of the actions of SO2n+1 and PSO2n+2 on self-adjoint operators and show how they facilitate in computing the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational Weierstrass point, and the average order of the 2-Selmer groups of Jacobians of hyperelliptic curves with a rational non-Weierstrass point, over arbitrary number fields. / Mathematics

published_or_final_version / Mathematics / Master / Master of Arts

No description available.

Although galaxy interactions cause dramatic changes, galaxies also continue to form stars and evolve when they are isolated. The dark matter (DM) halo may influence this evolution since it generates the rotational behaviour of galactic disks which could affect local conditions in the gas. Therefore we study neutral hydrogen kinematics of non-interacting, nearby spiral galaxies, characterising their rotation curves (RC) which probe the DM halo; delineating kinematic classes of galaxies; and investigating relations between these classes and galaxy properties such as disk size and star formation rate (SFR). To generate the RCs, we use GalAPAGOS (by J. Fiege). My role was to test and help drive the development of this software, which employs a powerful genetic algorithm, constraining 23 parameters while using the full 3D data cube as input. The RC is here simply described by a tanh-based function which adequately traces the global RC behaviour. Extensive testing on artificial galaxies show that the kinematic properties of galaxies with inclination >40 degrees, including edge-on galaxies, are found reliably. Using a hierarchical clustering algorithm on parametrised RCs from 79 galaxies culled from literature generates a preliminary scheme consisting of five classes. These are based on three parameters: maximum rotational velocity, turnover radius and outer slope of the RC. To assess the relationship between DM content and the kinematic classes, we generate mass models for 10 galaxies from the THINGS and WHISP surveys, and J. Irwin's sample. In most cases mass models using GalAPAGOS RCs were similar to those using traditional ``tilted-ring'' method RCs. The kinematic classes are mainly distinguished by their rotational velocity. We confirm correlations between increasing velocity and B-magnitude, optical disk size, and find earlier type galaxies among the strong rotators. SFR also increases with maximum rotational velocity. Given our limited subsample, we cannot discern a trend of velocity with DM halo properties such as M_halo/M_baryon. Using this strategy on upcoming large databases should reveal relationships between the DM halo and our kinematic classification scheme. If NGC 2841, NGC 3521 and NGC 5055 are understood to have declining RC after further investigation, this cannot be explained by the usual morphology scenarios.

Although galaxy interactions cause dramatic changes, galaxies also continue to form stars and evolve when they are isolated. The dark matter (DM) halo may influence this evolution since it generates the rotational behaviour of galactic disks which could affect local conditions in the gas. Therefore we study neutral hydrogen kinematics of non-interacting, nearby spiral galaxies, characterising their rotation curves (RC) which probe the DM halo; delineating kinematic classes of galaxies; and investigating relations between these classes and galaxy properties such as disk size and star formation rate (SFR). To generate the RCs, we use GalAPAGOS (by J. Fiege). My role was to test and help drive the development of this software, which employs a powerful genetic algorithm, constraining 23 parameters while using the full 3D data cube as input. The RC is here simply described by a tanh-based function which adequately traces the global RC behaviour. Extensive testing on artificial galaxies show that the kinematic properties of galaxies with inclination >40 degrees, including edge-on galaxies, are found reliably. Using a hierarchical clustering algorithm on parametrised RCs from 79 galaxies culled from literature generates a preliminary scheme consisting of five classes. These are based on three parameters: maximum rotational velocity, turnover radius and outer slope of the RC. To assess the relationship between DM content and the kinematic classes, we generate mass models for 10 galaxies from the THINGS and WHISP surveys, and J. Irwin's sample. In most cases mass models using GalAPAGOS RCs were similar to those using traditional ``tilted-ring'' method RCs. The kinematic classes are mainly distinguished by their rotational velocity. We confirm correlations between increasing velocity and B-magnitude, optical disk size, and find earlier type galaxies among the strong rotators. SFR also increases with maximum rotational velocity. Given our limited subsample, we cannot discern a trend of velocity with DM halo properties such as M_halo/M_baryon. Using this strategy on upcoming large databases should reveal relationships between the DM halo and our kinematic classification scheme. If NGC 2841, NGC 3521 and NGC 5055 are understood to have declining RC after further investigation, this cannot be explained by the usual morphology scenarios.

No description available.

This thesis presents novel, robust, analytic and algorithmic methods for calculating Bayesian posterior intervals of receiver operating characteristic (ROC) curves and confusion matrices used for the evaluation of intelligent medical systems tested with small amounts of data. Intelligent medical systems are potentially important in encapsulating rare and valuable medical expertise and making it more widely available. The evaluation of intelligent medical systems must make sure that such systems are safe and cost effective. To ensure systems are safe and perform at expert level they must be tested against human experts. Human experts are rare and busy which often severely restricts the number of test cases that may be used for comparison. The performance of expert human or machine can be represented objectively by ROC curves or confusion matrices. ROC curves and confusion matrices are complex representations and it is sometimes convenient to summarise them as a single value. In the case of ROC curves, this is given as the Area Under the Curve (AUC), and for confusion matrices by kappa, or weighted kappa statistics. While there is extensive literature on the statistics of ROC curves and confusion matrices they are not applicable to the measurement of intelligent systems when tested with small data samples, particularly when the AUC or kappa statistic is high. A fundamental Bayesian study has been carried out, and new methods devised, to provide better statistical measures for ROC curves and confusion matrices at low sample sizes. They enable exact Bayesian posterior intervals to be produced for: (1) the individual points on a ROC curve; (2) comparison between matching points on two uncorrelated curves; . (3) the AUC of a ROC curve, using both parametric and nonparametric assumptions; (4) the parameters of a parametric ROC curve; and (5) the weight of a weighted confusion matrix. These new methods have been implemented in software to provide a powerful and accurate tool for developers and evaluators of intelligent medical systems in particular, and to a much wider audience using ROC curves and confusion matrices in general. This should enhance the ability to prove intelligent medical systems safe and effective and should lead to their widespread deployment. The mathematical and computational methods developed in this thesis should also provide the basis for future research into determination of posterior intervals for other statistics at small sample sizes.