In 1990, Thurston proved that for any two-dimensional simply connected region, the space of tilings is flip-connected. Later, Yamzon reproved this result using a commutative …
Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for …
With the phrases “artificial intelligence” and “Deep Learning” surfacing in the news alongside projections of rampant automation, this paper aims to explore Deep Learning in …
This thesis concerns the formulation and derivation of a generalization of a collection of basis functions originally devised by Norbert Wiener for function approximation over …
Computer models for underwater sound propagation often rely on ray tracing to obtain solutions to the high frequency wave equation. While adequate for large scale …
Electroencephalography (EEG) signals are created by electrical currents from pyramidal neurons in the outer layer of the brain. These signals are easy to obtain and …
The first part of the thesis presents the surface respresentation of blood vessel walls extracted from medical images, sensitivity to the inlet/outlet boundary conditions, and …
We combine the spectral element method with the smoothed profile method (SPM) to obtain an efficient method for flows with moving boundaries in complex geometries. …
nheritable differences in DNA sequence are a major focus of the genetic community, as such differences are known to play a role in phenotypic variation, …
As a malaria patient takes and metabolizes weekly doses of an anti-malarial pyrimethamine, there is a periodic change in drug concentration. The growth rate, or …
Electronic Health Records (EHRs) have become the primary form of medical data-keeping across the United States. Federal law restricts the sharing of any EHR data …
High-order methods are emerging in the scientific computing community as superior alternatives to the classical finite difference, finite volume, and continuous finite element methods. The …
The mesoscopic description of molecular systems is investigated by using the memory function approach, and uncertainty quantification methods are developed for the evaluation of time …
This thesis is a large deviations study for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a …
Abstract Introduction: Cancer is a leading cause of death worldwide, accounting for 8.8 million deaths in 2015, and among which Lung Cancer consists 1.69 million …
Maximum likelihood estimators have traditionally dominated discrete inference for a long time. In this work we apply statistical decision theory to derive a new contender …
This thesis is a mathematical study of paleoclimatology and computational biology.<br/><br/> <br/><br/> Part I gives an introduction and overview of this dissertation.<br/><br/> <br/><br/> Part II presents the …
Studies in paleoclimatology should be accompanied by uncertainty analyses, as uncertainty is found within the very first measurements of the proxies imprinted in geological records. …
Non-allelic homologous recombination (NAHR) plays a major role in genome rearrangement and is implicated in numerous genetic disorders. But detection of NAHR poses a serious …
This dissertation presents two topics concerning weighted essentially non-oscillatory (WENO) finite difference schemes for solving hyperbolic problems. In the first part, we develop a high …