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 …
In this thesis, we study Prandtl's boundary layer theory for 2D, stationary, incompressible Navier-Stokes flows posed on domains with boundaries. The boundary layer hypothesis posed …
In many real-world applications, e.g., brain imaging and or weather patterns, data are captured over particular periods or intervals, which we call time series. Time …
We begin by asking how to write down Brownian motion on certain quotient Riemannian manifolds. The projection formula for the Laplace-Beltrami operator through Riemannian submersions …
Motile bacteria swim in fluid environments propelled by one or more flagella, spiral filaments that are attached to the cell body and a rotary motor. …
Burgers turbulence (1-D inviscid Burgers equation with random initial data) is a fundamental non-equilibrium model of stochastic coalescence. In this work we demonstrate that at …
We consider a discrete attachment model for the self-assembly of polyhedra called the Building Game. The combinatorial configuration space of the model is computed for …
Meshless methods provide an ideal framework for scalably simulating Lagrangian hydrodynamics in domains undergoing large deformation. For these schemes, interfaces can easily be treated without …
The problem of detecting changes in images taken by a stationary camera has been well studied and many algorithms now exist which perform robustly in …
This thesis is a mathematical and statistical study of conditional modeling and conditional inference. Two applications are covered: (1) Stock Prices and the Statistics of …
Confluence is an important property in many combinatorial processes. A globally confluent process is one in which a fixed initial state always leads to a …
Representation and comparison of shapes is a central problem in computer vision. In this dissertation, we continue investigation of a relatively recent approach, based on …
A space filling curve (or mapping) is a parametric map from a one-dimensional unit interval to a n-dimensional hypercube that traverses every point in its …
Abstract of Data-Driven Mathematical Analysis with Applications in Dynamical Systems, Biology, and Social Justice, by Rebecca Santorella Ph.D., Brown University, May 2022. As data becomes …
This thesis takes aim at two directions. The first direction involves setting the foundations for a new type of data-driven scientific computing, essentially creating a …
A number of problems of interest in applied mathematics and biology involve the quantification of uncertainty in computational and real-world models. A recent approach to …