We discover a new, curvature-localizing, subcritical buckling mode that produces a shallow-kink configuration in multi-layer graphene. Our density functional theory (DFT) analysis reveals the mode …
Volcanic hazards monitoring relies heavily on constraints offered by geophysical inversions to decipher the structure of subvolcanic magmatic systems. Over the past decades a multidisciplinary …
We extend the results presented by Antos et al. [1] for nonparametric estimation methods using complete datasets to nonparametric regression estimators that use right censored …
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 …
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 …
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 …
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 …
Abstract of Homoclinic Snaking of Spatiotemporal Patterns in Reaction Diffusion Equations, by Timothy V Roberts, Ph.D., Brown University, May 2024. Spiral and target waves are …
Diabetes is the leading cause of chronic kidney disease and kidney failure worldwide, causing 44 percent of new cases of kidney failure each year. Although …
Droplet impacts are of fundamental importance to the natural water cycle as collision and coalescence of droplets are the primary mechanism by which warm rain …
The spread of infectious disease is strongly influenced by human interaction. In order to understand this connection and develop effective strategies against future outbreaks, it …
As data structures become larger and more complex, methods of data analysis must evolve to harness the most accurate insights. Inspired by the challenges presented …
The focus of this dissertation is on the invertibility of certain topological summary statistics for metric objects. The first set of results concern persistence diagrams …
The field of computer assisted radiology has recently seen an explosion of novel techniques that have been made possible due to advancements in computer algorithms. …
This dissertation aims to develop several statistical methods for learning the manifold and topology structures of data, provide the corresponding theoretical foundations, and apply the …
Many real-world complex systems exhibit dynamics on network structures. Within such systems, patterns emerge in various ways and motivate diverse approaches towards understanding the formation …
Principal manifolds are used to represent high-dimensional data in a low-dimensional space. They are higher dimensional generalizations of principal curves and surfaces. The existing methods …
Abstract of “Problems at the interface of high dimensional probability and random matrix theory”, by Xiaoyu Xie, Ph.D., Brown University, May 2024 In this thesis, …
