Forecasting U.S. elections has been a field of interest for many researchers, with various statistical and mathematical models being proposed. In my research, I analyzed a prior election model, the SIS election model. In this model, a system of differential equations traditionally used in epidemiology to study disease transmission (but...
Forecasting the outcomes of U.S. elections is a relevant and complex task that has been approached in many ways, most commonly incorporating statistics or proprietary methods that include some degree of subjectivity. Our approach differs from this convention in that we use multidisciplinary methods from applied mathematics. Specifically, we use...
To survive, animals, including human beings, have developed an amazing ability to learn the constantly changing environment. Specifically, detecting specific odorants in a noisy, variable background is crucial for finding food and water, mating, and avoiding potential dangers. For this purpose, rodents have developed an olfactory system that is powerful...
This dissertation considers a periodically-forced 1-D Langevin equation that possesses two stable periodic solutions in the absence of noise. We aim at answering the question: is there a most likely noise-induced transition path between these periodic solutions that allows one to identify a preferred phase of the forcing when the...
Many industrial fluid flow problems involve the interaction between heavy, rigid objects and one or more fluid phases. For several decades, there has been a vested interest in simulating these fluid-structure interaction (FSI) problems in order to improve engineering design processes. However, numerical simulations of these problems can be challenging...
This dissertation presents two projects with the goal of understanding how to quantitatively describe biological data, particularly data that is highly dynamic. The first study presents an improved quantitative tool for the analysis of particulate trajectories. Particulate trajectory data appears in several different biological contexts, and the majority of analyses...
Gene regulatory networks (GRNs) are important abstractions of the complex regulatory interplays between genes, proteins, metabolites, and other molecular-level entities. Comprehensive GRNs provide high-level overviews of the topology of gene-gene interactions and their purposes, thereby enabling a comprehensive understanding of their role in phenotypic variation, disease mechanisms, and other biological...
This thesis focuses on the application of neural networks to three types of classification tasks, each work with its own chapter. The objective of the first work is to take advantage of deep neural networks in order to make next day crime count predictions in a fine-grain city partition. We...