Physical Sciences and Mathematics Commons^™

High-Performance Computing In Covariant Loop Quantum Gravity, Pietropaolo Frisoni

Electronic Thesis and Dissertation Repository

This Ph.D. thesis presents a compilation of the scientific papers I published over the last three years during my Ph.D. in loop quantum gravity (LQG). First, we comprehensively introduce spinfoam calculations with a practical pedagogical paper. We highlight LQG's unique features and mathematical formalism and emphasize the computational complexities associated with its calculations. The subsequent articles delve into specific aspects of employing high-performance computing (HPC) in LQG research. We discuss the results obtained by applying numerical methods to studying spinfoams' infrared divergences, or ``bubbles''. This research direction is crucial to define the continuum limit of LQG properly. We investigate the …

Data-Driven Exploration Of Coarse-Grained Equations: Harnessing Machine Learning, Elham Kianiharchegani

Electronic Thesis and Dissertation Repository

In scientific research, understanding and modeling physical systems often involves working with complex equations called Partial Differential Equations (PDEs). These equations are essential for describing the relationships between variables and their derivatives, allowing us to analyze a wide range of phenomena, from fluid dynamics to quantum mechanics. Traditionally, the discovery of PDEs relied on mathematical derivations and expert knowledge. However, the advent of data-driven approaches and machine learning (ML) techniques has transformed this process. By harnessing ML techniques and data analysis methods, data-driven approaches have revolutionized the task of uncovering complex equations that describe physical systems. The primary goal in …

Dynamically Finding Optimal Kernel Launch Parameters For Cuda Programs, Taabish Jeshani

Electronic Thesis and Dissertation Repository

In this thesis, we present KLARAPTOR (Kernel LAunch parameters RAtional Program estimaTOR), a freely available tool to dynamically determine the values of kernel launch parameters of a CUDA kernel. We describe a technique for building a helper program, at the compile-time of a CUDA program, that is used at run-time to determine near-optimal kernel launch parameters for the kernels of that CUDA program. This technique leverages the MWP-CWP performance prediction model, runtime data parameters, and runtime hardware parameters to dynamically determine the launch parameters for each kernel invocation. This technique is implemented within the KLARAPTOR tool, utilizing the LLVM Pass …

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …

Nearby Galaxies: Modelling Star Formation Histories And Contamination By Unresolved Background Galaxies, Hadi Papei

Electronic Thesis and Dissertation Repository

Galaxies are complex systems of stars, gas, dust, and dark matter which evolve over billions of years, and one of the main goals of astrophysics is to understand how these complex systems form and change. Measuring the star formation history of nearby galaxies, in which thousands of stars can be resolved individually, has provided us with a clear picture of their evolutionary history and the evolution of galaxies in general.

In this work, we have developed the first public Python package, SFHPy, to measure star formation histories of nearby galaxies using their colour-magnitude diagrams. In this algorithm, an observed colour-magnitude …

Three Contributions To The Theory And Practice Of Optimizing Compilers, Linxiao Wang

Electronic Thesis and Dissertation Repository

The theory and practice of optimizing compilers gather techniques that, from input computer programs, aim at generating code making the best use of modern computer hardware. On the theory side, this thesis contributes new results and algorithms in polyhedral geometry. On the practical side, this thesis contributes techniques for the tuning of parameters of programs targeting GPUs. We detailed these two fronts of our work below.

Consider a convex polyhedral set P given by a system of linear inequalities A*x <= b, where A is an integer matrix and b is an integer vector. We are interested in the integer hull P_I of P which is the smallest convex polyhedral set that contains all the integer points in P. In Chapter …

The Design And Implementation Of A High-Performance Polynomial System Solver, Alexander Brandt

Electronic Thesis and Dissertation Repository

This thesis examines the algorithmic and practical challenges of solving systems of polynomial equations. We discuss the design and implementation of triangular decomposition to solve polynomials systems exactly by means of symbolic computation.

Incremental triangular decomposition solves one equation from the input list of polynomials at a time. Each step may produce several different components (points, curves, surfaces, etc.) of the solution set. Independent components imply that the solving process may proceed on each component concurrently. This so-called component-level parallelism is a theoretical and practical challenge characterized by irregular parallelism. Parallelism is not an algorithmic property but rather a geometrical …

A Molecular Dynamics Study Of Polymer Chains In Shear Flows And Nanocomposites, Venkat Bala

Electronic Thesis and Dissertation Repository

In this work we study single chain polymers in shear flows and nanocomposite polymer melts extensively through the use of large scale molecular dynamics simulations through LAMMPS. In the single polymer chain shear flow study, we use the Lattice Boltzmann method to simulate fluid dynamics and also include thermal noise as per the \emph{fluctuation-dissipation} theorem in the system. When simulating the nanocomposite polymer melts, we simply use a Langevin thermostat to mimic a heat bath. In the single polymer in shear flow study we investigated the margination of a single chain towards solid surfaces and how strongly the shear flow …

Cache-Friendly, Modular And Parallel Schemes For Computing Subresultant Chains, Mohammadali Asadi

Electronic Thesis and Dissertation Repository

The RegularChains library in Maple offers a collection of commands for solving polynomial systems symbolically with taking advantage of the theory of regular chains. The primary goal of this thesis is algorithmic contributions, in particular, to high-performance computational schemes for subresultant chains and underlying routines to extend that of RegularChains in a C/C++ open-source library.

Subresultants are one of the most fundamental tools in computer algebra. They are at the core of numerous algorithms including, but not limited to, polynomial GCD computations, polynomial system solving, and symbolic integration. When the subresultant chain of two polynomials is involved in a client …

Parallel Arbitrary-Precision Integer Arithmetic, Davood Mohajerani

Electronic Thesis and Dissertation Repository

Arbitrary-precision integer arithmetic computations are driven by applications in solving systems of polynomial equations and public-key cryptography. Such computations arise when high precision is required (with large input values that fit into multiple machine words), or to avoid coefficient overflow due to intermediate expression swell. Meanwhile, the growing demand for faster computation alongside the recent advances in the hardware technology have led to the development of a vast array of many-core and multi-core processors, accelerators, programming models, and language extensions (e.g. CUDA, OpenCL, and OpenACC for GPUs, and OpenMP and Cilk for multi-core CPUs). The massive computational power of parallel …

Longitudinal Partitioning Waveform Relaxation Methods For The Analysis Of Transmission Line Circuits, Tarik Menkad

Electronic Thesis and Dissertation Repository

Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits.

The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic …

Edge-Cloud Iot Data Analytics: Intelligence At The Edge With Deep Learning, Ananda Mohon M. Ghosh

Electronic Thesis and Dissertation Repository

Rapid growth in numbers of connected devices, including sensors, mobile, wearable, and other Internet of Things (IoT) devices, is creating an explosion of data that are moving across the network. To carry out machine learning (ML), IoT data are typically transferred to the cloud or another centralized system for storage and processing; however, this causes latencies and increases network traffic. Edge computing has the potential to remedy those issues by moving computation closer to the network edge and data sources. On the other hand, edge computing is limited in terms of computational power and thus is not well suited for …

Physical Dispersions Of Meteor Showers Through High Precision Optical Observations, Denis Vida

Electronic Thesis and Dissertation Repository

Meteoroids ejected from comets form meteoroid streams which disperse over time due to gravitational perturbations and non-gravitational forces. When stream meteoroids collide with the Earth's atmosphere, they are visible as meteors emanating from a common point-like area (radiant) in the sky. Measuring the size of meteor shower radiant areas can provide insight into stream formation and age. The tight radiant dispersion of young streams are difficult to determine due to measurement error, but if successfully measured, the dispersion could be used to constrain meteoroid ejection velocities from their parent comets. The estimated ejection velocity is an uncertain, model-dependent value with …

A Visual Analytics System For Making Sense Of Real-Time Twitter Streams, Amir Haghighatimaleki

Electronic Thesis and Dissertation Repository

Through social media platforms, massive amounts of data are being produced. Twitter, as one such platform, enables users to post “tweets” on an unprecedented scale. Once analyzed by machine learning (ML) techniques and in aggregate, Twitter data can be an invaluable resource for gaining insight. However, when applied to real-time data streams, due to covariate shifts in the data (i.e., changes in the distributions of the inputs of ML algorithms), existing ML approaches result in different types of biases and provide uncertain outputs. This thesis describes a visual analytics system (i.e., a tool that combines data visualization, human-data interaction, and …

Vertical Ionization Energies From The Average Local Electron Energy Function, Amer Marwan El-Samman

Electronic Thesis and Dissertation Repository

It is a non-intuitive but well-established fact that the first and higher vertical ionization energies (VIE) of any N-electron system are encoded in the system's ground-state electronic wave function. This makes it possible to compute VIEs of any atom or molecule from its ground-state wave function directly, without performing calculations on the (N-1)-electron states. In practice, VIEs can be extracted from the wave function by using the (extended) Koopmans' theorem or by taking the asymptotic limit of certain wave-function-based quantities such as the ratio of kinetic energy density to the electron density. However, when the wave function is expanded in …

High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt

Electronic Thesis and Dissertation Repository

Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit …

From Large-Scale Molecular Clouds To Filaments And Cores : Unveiling The Role Of The Magnetic Fields In Star Formation, Sayantan Auddy

Electronic Thesis and Dissertation Repository

I present a comprehensive study of the role of strong magnetic fields in characterizing the structure of molecular clouds. We run three-dimensional turbulent non-ideal magnetohydrodynamic simulations (with ambipolar diffusion) to see the effect of magnetic fields on the evolution of the column density probability distribution function (PDF). Our results indicate a systematic dependence of the column density PDF of molecular clouds on magnetic field strength and turbulence, with observationally distinguishable outcomes between supercritical (gravity dominated) and subcritical (magnetic field dominated) initial conditions. We find that most cases develop a direct power-law PDF, and only the subcritical clouds with turbulence are …

Analysis Challenges For High Dimensional Data, Bangxin Zhao

Electronic Thesis and Dissertation Repository

In this thesis, we propose new methodologies targeting the areas of high-dimensional variable screening, influence measure and post-selection inference. We propose a new estimator for the correlation between the response and high-dimensional predictor variables, and based on the estimator we develop a new screening technique termed Dynamic Tilted Current Correlation Screening (DTCCS) for high dimensional variables screening. DTCCS is capable of picking up the relevant predictor variables within a finite number of steps. The DTCCS method takes the popular used sure independent screening (SIS) method and the high-dimensional ordinary least squares projection (HOLP) approach as its special cases.

Two methods …

Some Applications Of Higher-Order Hidden Markov Models In The Exotic Commodity Markets, Heng Xiong

Electronic Thesis and Dissertation Repository

The liberalisation of regional and global commodity markets over the last several decades resulted in certain commodity price behaviours that require new modelling and estimation approaches. Such new approaches have important implications to the valuation and utilisation of commodity derivatives. Derivatives are becoming increasingly crucial for market participants in hedging their exposure to volatile price swings and in managing risks associated with derivative trading. The modelling of commodity-based variables is an integral part of risk management and optimal-investment strategies for commodity-linked portfolios. The characteristics of commodity price evolution cannot be captured sufficiently by one-state driven models even with the inclusion …

Feasible Computation In Symbolic And Numeric Integration, Robert H.C. Moir

Electronic Thesis and Dissertation Repository

Two central concerns in scientific computing are the reliability and efficiency of algorithms. We introduce the term feasible computation to describe algorithms that are reliable and efficient given the contextual constraints imposed in practice. The main focus of this dissertation then, is to bring greater clarity to the forms of error introduced in computation and modeling, and in the limited context of symbolic and numeric integration, to contribute to integration algorithms that better account for error while providing results efficiently.

Chapter 2 considers the problem of spurious discontinuities in the symbolic integration problem, proposing a new method to restore continuity …

Simulation Of Driven Elastic Spheres In A Newtonian Fluid, Shikhar M. Dwivedi

Electronic Thesis and Dissertation Repository

Simulations help us test various restrictions/assumptions placed on physical systems that would otherwise be difficult to efficiently explore experimentally. For example, the Scallop Theorem, first stated in 1977, places limitations on the propulsion mechanisms available to microscopic objects in fluids. In particular, the theorem states that when the viscous forces in a fluid dominate the inertial forces associated with a physical body, such a physical body cannot generate propulsion by means of reciprocal motion. The focus of this thesis is to firstly, explore an adaptive Multiple-timestep(MTS) scheme for faster molecular dynamics(MD) simulations, and secondly, use hybrid MD-LBM(Lattice-Boltzman Method) to test …

Mining Of Primary Healthcare Patient Data With Selective Multimorbid Diseases, Annette Megerdichian Azad

Electronic Thesis and Dissertation Repository

Despite a large volume of research on the prognosis, diagnosis and overall burden of multimorbidity, very little is known about socio-demographic characteristics of multimorbid patients. This thesis aims to analyze the socio-demographic characteristics of patients with multiple chronic conditions (multimorbidity), focusing on patient groups sharing the same combination of diseases. Several methods were explored to analyze the co-occurrence of multiple chronic diseases as well as the associations between socio-demographics and chronic conditions. These methods include disease pair distributions over gender, age groups and income level quintiles, Multimorbidity Coefficients for measuring the concurrence of disease pairs and triples, and k-modes clustering …

Towards Comprehensive Parametric Code Generation Targeting Graphics Processing Units In Support Of Scientific Computation, Ning Xie

Electronic Thesis and Dissertation Repository

The most popular multithreaded languages based on the fork-join concurrency model (CIlkPlus, OpenMP) are currently being extended to support other forms of parallelism (vectorization, pipelining and single-instruction-multiple-data (SIMD)). In the SIMD case, the objective is to execute the corresponding code on a many-core device, like a GPGPU, for which the CUDA language is a natural choice. Since the programming concepts of CilkPlus and OpenMP are very different from those of CUDA, it is desirable to automatically generate optimized CUDA-like code from CilkPlus or OpenMP.

In this thesis, we propose an accelerator model for annotated C/C++ code together with an implementation …

Development Of Anatomical And Functional Magnetic Resonance Imaging Measures Of Alzheimer Disease, Samaneh Kazemifar

Electronic Thesis and Dissertation Repository

Alzheimer disease is considered to be a progressive neurodegenerative condition, clinically characterized by cognitive dysfunction and memory impairments. Incorporating imaging biomarkers in the early diagnosis and monitoring of disease progression is increasingly important in the evaluation of novel treatments. The purpose of the work in this thesis was to develop and evaluate novel structural and functional biomarkers of disease to improve Alzheimer disease diagnosis and treatment monitoring. Our overarching hypothesis is that magnetic resonance imaging methods that sensitively measure brain structure and functional impairment have the potential to identify people with Alzheimer’s disease prior to the onset of cognitive decline. …

Identifying Individual Driver Behaviour Using In-Vehicle Can-Bus Signals Of Pre-Turning Maneuvers, Mahboubeh Zardosht

Electronic Thesis and Dissertation Repository

All drivers have their own driving style while performing different driving maneuvers. They vary in using vehicle’s control devices such as the steering wheel, pedals, gears etc. In this thesis, we analyze driving behavior in different timeframes prior to turns. We employ data obtained from actual driving behavior in an urban environment collected from the CAN-Bus of an instrumented vehicle. Five CAN-Bus signals, vehicle speed, gas pedal pressure, brake pedal pressure, steering wheel angle, and acceleration, is collected for 5, 10, and 15 seconds of driving prior to each turn. We consider all turns for each driver as well as …

Tropical Cyclone Wind Hazard Assessment For Southeast Part Of Coastal Region Of China, Sihan Li

Electronic Thesis and Dissertation Repository

Tropical cyclone (TC) or typhoon wind hazard and risk are significant for China. The return period value of the maximum typhoon wind speed is used to characterize the typhoon wind hazard and assign wind load in building design code. Since the historical surface observations of typhoon wind speed are often scarce and of short period, the typhoon wind hazard assessment is often carried out using the wind field model and TC track model. For a few major cities in the coastal region of mainland China, simple or approximated wind field models and a circular subregion method (CSM) have been used …

Automated Image Interpretation For Science Autonomy In Robotic Planetary Exploration, Raymond Francis

Electronic Thesis and Dissertation Repository

Advances in the capabilities of robotic planetary exploration missions have increased the wealth of scientific data they produce, presenting challenges for mission science and operations imposed by the limits of interplanetary radio communications. These data budget pressures can be relieved by increased robotic autonomy, both for onboard operations tasks and for decision- making in response to science data.

This thesis presents new techniques in automated image interpretation for natural scenes of relevance to planetary science and exploration, and elaborates autonomy scenarios under which they could be used to extend the reach and performance of exploration missions on planetary surfaces.

Two …

On The Applications Of Lifting Techniques, Esmaeil Mehrabi

Electronic Thesis and Dissertation Repository

Lifting techniques are some of the main tools in solving a variety of different computational problems related to the field of computer algebra. In this thesis, we will consider two fundamental problems in the fields of computational algebraic geometry and number theory, trying to find more efficient algorithms to solve such problems.

The first problem, solving systems of polynomial equations, is one of the most fundamental problems in the field of computational algebraic geometry. In this thesis, We discuss how to solve bivariate polynomial systems over either k(T ) or Q using a combination of lifting and modular composition techniques. …

The Electrochemistry Of Hydrogen Peroxide On Uranium Dioxide And The Modelling Of Used Nuclear Fuel Corrosion Under Permanent Disposal Conditions, Linda Wu

Electronic Thesis and Dissertation Repository

This thesis reports a series of investigations examining the corrosion process of used nuclear fuel under permanent disposal conditions. The motivation of the project is that the safety assessment of deep geological disposal of spent nuclear fuel requires a fundamental understanding of the processes controlling fuel corrosion which could lead to the release of radionuclides to the geosphere from a failed container.

One primary objective of this project was to develop a computational model in order to simulate fuel corrosion under the disposal conditions. A series of simulations based on COMSOL were designed and developed to determine the influence of …

Image Fusion And Axial Labeling Of The Spine, Brandon Miles

Electronic Thesis and Dissertation Repository

In order to improve radiological diagnosis of back pain and spine disease, two new algorithms have been developed to aid the 75% of Canadians who will suffer from back pain in a given year. With the associated medical imaging required for many of these patients, there is a potential for improvement in both patient care and healthcare economics by increasing the accuracy and efficiency of spine diagnosis. A real-time spine image fusion system and an automatic vertebra/disc labeling system have been developed to address this. Both magnetic resonance (MR) images and computed tomography (CT) images are often acquired for patients. …