Applied Mathematics Commons^™

Non-Equispaced Fast Fourier Transforms In Turbulence Simulation, Aditya M. Kulkarni

Masters Theses

Fourier pseudo-spectral method on equispaced grid is one of the approaches in turbulence simulation, to compute derivative of discrete data, using fast Fourier Transform (FFT) and gives low dispersion and dissipation errors. In many turbulent flows the dynamically important scales of motion are concentrated in certain regions which requires a coarser grid for higher accuracy. A coarser grid in other regions minimizes the memory requirement. This requires the use of Non-equispaced Fast Fourier Transform (NFFT) to compute the Fourier transform, by solving a system of linear equations.

To achieve similar accuracy, the NFFT needs to return more Fourier coefficients than …

A Review Of Random Matrix Theory With An Application To Biological Data, Jesse Aaron Marks

Masters Theses

"Random matrix theory (RMT) is an area of study that has applications in a wide variety of scientific disciplines. The foundation of RMT is based on the analysis of the eigenvalue behavior of matrices. The eigenvalues of a random matrix (a matrix with stochastic entries) will behave differently than the eigenvalues from a matrix with non-random properties. Studying this bifurcation of the eigenvalue behavior provides the means to which system-specific signals can be distinguished from randomness. In particular, RMT provides an algorithmic approach to objectively remove noise from matrices with embedded signals.

Major advances in data acquisition capabilities have changed …

The Pantograph Equation In Quantum Calculus, Thomas Griebel

Masters Theses

"In this thesis, the pantograph equation in quantum calculus is investigated. The pantograph equation is a famous delay differential equation that has been known since 1971. Till the present day, the continuous and the discrete cases of the pantograph equation are well studied. This thesis deals with different pantograph equations in quantum calculus. An explicit solution representation and the exponential behavior of solutions of a pantograph equation are proved. Furthermore, several pantograph equations regarding asymptotic stability are considered. In fact, conditions for the asymptotic stability of the zero solution are derived and subsequently illustrated by examples. Moreover, an explicit solution …

Family-Based Association Studies Of Autism In Boys Via Facial-Feature Clusters, Luke Andrew Settles

Masters Theses

"Autism spectrum disorder (ASD) refers to a set of developmental disorders with varied attributes. Due to its substantial heterogeneity in terms of behavioral and clinical phenotypes, it is challenging to discern the genetic biomarkers behind ASD, even though the disease is known to be genetic in nature. This serves as a motivation to detect relationships between single nucleotide polymorphisms (SNPs) and a causal autism disease susceptibility locus (DSL) within more homogeneous subgroups. Recently, clinically meaningful subclassifications of ASD have been discovered utilizing facial features of prepubescent boys. Therefore, through the employment of data from 44 prepubertal Caucasian boys with ASD …