Physical Sciences and Mathematics Commons^™

Lattice Extensions And Zeros Of Multilinear Polynomials, Maxwell Forst

CGU Theses & Dissertations

We treat several problems related to the existence of lattice extensions preserving certain geometric properties and small-height zeros of various multilinear polynomials. An extension of a Euclidean lattice $L_1$ is a lattice $L_2$ of higher rank containing $L_1$ so that the intersection of $L_2$ with the subspace spanned by $L_1$ is equal to $L_1$. Our first result provides a counting estimate on the number of ways a primitive collection of vectors in a lattice can be extended to a basis for this lattice. Next, we discuss the existence of lattice extensions with controlled determinant, successive minima and covering radius. In …

On Symmetric Operator Ideals And S-Numbers, Daniel Akech Thiong

CGU Theses & Dissertations

Motivated by the well-known theorem of Schauder, we study the relationship between various s-numbers of an operator T and its adjoint T∗ between Banach spaces. For non-compact operator T ∈ L(X, Y ), we do not have a lot of information about the relationship between n-th s-number, sn(T), with sn(T∗ ), however, in chapter 2, by considering X and Y , with lifting and extension properties, respectively, we were able to obtain a relationship between sn(T) with sn(T∗ ) for certain …

On Coherence And The Geometry Of Certain Families Of Lattices, David Booth Kogan

CGU Theses & Dissertations

The coherence of a lattice is, roughly speaking, a measure of non-orthogonality of its minimal vectors. It was introduced to lattices (by analogy with frame theory) by L. Fukshansky and others as a possible route to gaining insight into packing density, a central problem in lattice theory. In this work, we introduce the related measure of average coherence, explore connections between packing density and coherence, and prove several properties of certain families of lattices, most notably nearly orthogonal lattices, cyclotomic lattices, and cyclic lattices.

On Multiplication Groups Of Quasigroups, Ahmed Al Fares

CGU Theses & Dissertations

Quasigroups are algebraic structures in which divisibility is always defined. In this thesis we investigate quasigroups using a group-theoretic approach. We first construct a family of quasigroups which behave in a group-like fashion. We then focus on the multiplication groups of quasigroups, which have first appeared in the work of A. A. Albert. These permutation groups allow us to study quasigroups using group theory. We also explore how certain natural operations on quasigroups affect the associated multiplication groups. Along the way we take the time and special care to pose specific questions that may lead to further work in the …

An Exponential Formula For Random Variables Generated By Multiple Brownian Motions, Maximilian Lawrence Baroi

CGU Theses & Dissertations

The frozen operator has been used to develop Dyson-series like representations for random variables generated by classical Brownian motion, Lévy processes and fractional Brownian with Hurst index greater than 1/2.The relationship between the conditional expectation of a random variable (or fractional conditional expectation in the case of fractional Brownian motion)and that variable's Dyson-series like representation is the exponential formula. These results had not yet been extended to either fractional Brownian motion with Hurst index less than 1/2, or d-dimensional Brownian motion. The former is still out of reach, but we hope our review of stochastic integration for fractional Brownian motion …

Measuring Machine Learning Model Uncertainty With Applications To Aerial Segmentation, Kevin James Cotton

CGU Theses & Dissertations

Machine learning model performance on both validation data and new data can be better measured and understood by leveraging uncertainty metrics at the time of prediction. These metrics can improve the model training process by indicating which training data need to be corrected and what part of the domain needs further annotation. The methods described have yet to reach mainstream adoption, and show great potential. Here, we survey the field of uncertainty metrics and provide a robust framework for its application to aerial segmentation. Uncertainty is divided into two types: aleatoric and epistemic. Aleatoric uncertainty arises from variations in training …

Spectral Analysis Of Complex Dynamical Systems, Casey Lynn Johnson

CGU Theses & Dissertations

The spectrum of any differential equation or a system of differential equations is related to several important properties about the problem and its subsequent solution. So much information is held within the spectrum of a problem that there is an entire field devoted to it; spectral analysis. In this thesis, we perform spectral analysis on two separate complex dynamical systems. The vibrations along a continuous string or a string with beads on it are the governed by the continuous or discrete wave equation. We derive a small-vibrations model for multi-connected continuous strings that lie in a plane. We show that …

Preliminary Study Of Highway Pavement And Materials, Omer Eljairi

CGU Theses & Dissertations

This preliminary study covered (a) the effects of in-place air voids and other factors on fatigue cracking using Long-Term Pavement Performance data, (b) fracture properties of asphalt concrete in a semicircular bend (SCB) test using a noncontact camera and crosshead movement, and (c) hot applied modified-binder-chip-seal field performance in California. The objective is to improve pavement performance and life, establish a quality assurance/quality control (QA/QC) tests of fracture properties of asphalt mixtures, and save millions of dollars on maintenance and rehabilitation. Chapter 1 investigated the effect of in-place air voids (AV), asphalt content (AC), bulk-specific gravity (BSG), and maximum specific …

Detection And Localization Of Linear Features Based On Image Processing Methods, Sean Cormick Matz

CGU Theses & Dissertations

In this work, the general problem of the detection of features in images is considered. One of the methods, the orientation detection of lines, utilized the Radon transform (sinogram) of an image to detect lines at different angles in an image. The line thickness algorithm was generated by finding a pattern formed by particular lines in an image. The filtering of reconstructed images dealt with the removal of blur and other artifacts that arose in the course of inverting the Radon transform of an image to attempt to obtain the original image.

Gait And Postural Analysis In Healthy Young Adults And People With Parkinson's Disease, Aisha Joy Chen

CGU Theses & Dissertations

Postural analysis is the study of how the position of the body in any mode interacts with internal and external forces. This type of analysis is typically used to assess potential abnormalities in the balance control system and to understand how the balance control system changes with time. However, compared to other medical fields of study, postural analysis is relatively new [1]. In fact, although widely used in clinical and research studies, postural assessment methods are scientifically inaccurate, and some data collection methods are relatively expensive. A better understanding of the human balance control system could lead to more accurate …

Free Market On The Free Way, Yuan Cheng

CGU Theses & Dissertations

Self-driving cars have the potential to decrease congestion and will probably become the future of efficient transportation. This dissertation presents a unique approach to implement sharing lanes on a freeway using the idea of option pricing. A macroscopic physical model (LWR) is implemented by adding noise to the speed which accounts for unexpected events. We then proceed to provide a fair price for lanes in real time.

Wireless Channel Equalization In Digital Communication Systems, Sammuel Jalali

CGU Theses & Dissertations

Our modern society has transformed to an information-demanding system, seeking voice, video, and data in quantities that could not be imagined even a decade ago. The mobility of communicators has added more challenges. One of the new challenges is to conceive highly reliable and fast communication system unaffected by the problems caused in the multipath fading wireless channels. Our quest is to remove one of the obstacles in the way of achieving ultimately fast and reliable wireless digital communication, namely Inter-Symbol Interference (ISI), the intensity of which makes the channel noise inconsequential.

The theoretical background for wireless channels modeling and …

Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering, David Caballero

CGU Theses & Dissertations

There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for …