Higher Derivative Gravitational Systems and Ghost Fields

Effective Field Theory (EFT) is one of the most powerful theoretical tools in the hands of cosmologists, it allows them to come up with testable effective descriptions of the universe even when a fundamental theory is missing. EFT though, is not the only possible answer for pushing our knowledge beyond the limits of what has already been established. Applying EFT and other alternative methods has become an important part of a cosmologist’s work, particularly in the last few years when a vast plethora of extensions of the Standard Model of Cosmology has been proposed and needs to be tested against experimental results. In this work we mainly investigate the limits of EFT in the context of cosmic acceleration, and the possibility of calculating corrections to the low energy standard cosmological results by re-interpreting the meaning of higher derivative terms in perturbation expansions

Visual Computing Tools for Studying Micro-scale Diffusion

In this dissertation, we present novel visual computing tools and techniques to facilitate the exploration, simulation, and visualization of micro-scale diffusion. Our research builds upon the latest advances in visualization, high-performance computing, medical imaging, and human perception. We validate our research using the driving applications of nano-assembly and diffusion kurtosis imaging (DKI). In both of these applications, diffusion plays a central role. In the former it mediates the process of transporting micron-sized particles through moving lasers, and in the latter it conveys brain micro-geometry. Nanocomponent-based devices, such as bio-sensors, electronic components, photonic devices, solar cells, and batteries, are expected to revolutionize health care, energy, communications, and the computing industry. However, in order to build such useful devices, nanoscale components need to be properly assembled together. We have developed a hybrid CPU/GPU-based computing tool to understand complex interactions between lasers, optical beads, and the suspension medium. We demonstrate how a high-performance visual computing tool can be used to accelerate an optical tweezers simulation to compute the force applied by a laser onto micro particles and study shadowing (refraction) behavior. This represents the first steps toward building a real-time nano-assembly planning system. A challenge in building such a system, however, is that optical tweezers systems typically lack stereo depth cues. We have developed a visual tool to provide an enhanced perception of a scene's 3D structure using the kinetic depth effect. The design of our tool has been informed by user studies of stereo perception using the kinetic-depth effect on monocular displays. Diffusion kurtosis imaging is gaining rapid adoption in the medical imaging community due to its ability to measure the non-Gaussian property of water diffusion in biological tissues. Compared with the traditional diffusion tensor imaging (DTI), DKI can provide additional details about the underlying microstructural characteristics of neural tissues. It has shown promising results in studies on changes in gray matter and mild traumatic brain injuries, where DTI is often found to be inadequate. However, the highly detailed spatio-angular fields in DKI datasets present a special challenge for visualization. Traditional techniques that use glyphs are often inadequate for expressing subtle changes in the DKI fields. In this dissertation, we outline a systematic way to manage, analyze, and visualize spatio-angular fields using spherical harmonics lighting functions to facilitate insights into the micro-structural properties of the brain

The astrometric core solution for the Gaia mission. Overview of models, algorithms and software implementation

The Gaia satellite will observe about one billion stars and other point-like sources. The astrometric core solution will determine the astrometric parameters (position, parallax, and proper motion) for a subset of these sources, using a global solution approach which must also include a large number of parameters for the satellite attitude and optical instrument. The accurate and efficient implementation of this solution is an extremely demanding task, but crucial for the outcome of the mission. We provide a comprehensive overview of the mathematical and physical models applicable to this solution, as well as its numerical and algorithmic framework. The astrometric core solution is a simultaneous least-squares estimation of about half a billion parameters, including the astrometric parameters for some 100 million well-behaved so-called primary sources. The global nature of the solution requires an iterative approach, which can be broken down into a small number of distinct processing blocks (source, attitude, calibration and global updating) and auxiliary processes (including the frame rotator and selection of primary sources). We describe each of these processes in some detail, formulate the underlying models, from which the observation equations are derived, and outline the adopted numerical solution methods with due consideration of robustness and the structure of the resulting system of equations. Appendices provide brief introductions to some important mathematical tools (quaternions and B-splines for the attitude representation, and a modified Cholesky algorithm for positive semidefinite problems) and discuss some complications expected in the real mission data.Comment: 48 pages, 19 figures. Accepted for publication in Astronomy & Astrophysic

Disparate View Matching

Matching of disparate views has gained significance in computer vision due to its role in many novel application areas. Being able to match images of the same scene captured during day and night, between a historic and contemporary picture of a scene, and between aerial and ground-level views of a building facade all enable novel applications ranging from loop-closure detection for structure-from-motion and re-photography to geo-localization of a street-level image using reference imagery captured from the air. The goal of this work is to develop novel features and methods that address matching problems where direct appearance-based correspondences are either difficult to obtain or infeasible because of the lack of appearance similarity altogether. To address these problems, we propose methods that span the appearance-geometry spectrum in terms of both the use of these cues as well as the ability of each method to handle variations in appearance and geometry. First, we consider the problem of geo-localization of a query street-level image using a reference database of building facades captured from a bird\u27s eye view. To address this wide-baseline facade matching problem, a novel scale-selective self-similarity feature that avoids direct comparison of appearance between disparate facade images is presented. Next, to address image matching problems with more extreme appearance variation, a novel representation for matchable images expressed in terms of the eigen-functions of the joint graph of the two images is presented. This representation is used to derive features that are persistent across wide variations in appearance. Next, the problem setting of matching between a street-level image and a digital elevation map (DEM) is considered. Given the limited appearance information available in this scenario, the matching approach has to rely more significantly on geometric cues. Therefore, a purely geometric method to establish correspondences between building corners in the DEM and the visible corners in the query image is presented. Finally, to generalize this problem setting we address the problem of establishing correspondences between 3D and 2D point clouds using geometric means alone. A novel framework for incorporating purely geometric constraints into a higher-order graph matching framework is presented with specific formulations for the three-point calibrated absolute camera pose problem (P3P), two-point upright camera pose problem (Up2p) and the three-plus-one relative camera pose problem