Promyelocytic leukemia (PML) nuclear bodies act as quality control centers in the nucleus, participating in a plethora of nuclear functions. As such, PML bodies are a signature model for functional nuclear organization. PML bodies have a dynamic protein composition that responds to changing conditions of the cell. Many of the...
We establish the criterion for chaos in three-planet systems, for systems similar to those discovered by the Kepler spacecraft. Our main results are as follows: (i) The simplest criterion, which is based on overlapping mean motion resonances (MMRs), only agrees with numerical simulations at a very crude level. (ii) Much...
Machine learning and deep learning have been proven successful across various scientific fields, such as computer vision, natural language processing, and recommendation systems. As models become more complex, with more parameters and intricate architectures, they can achieve higher prediction accuracy when trained on larger datasets. However, despite the great prediction...
The action of the automorphisms of a formal group on its deformation space is crucial to understanding periodic families in the homotopy groups of spheres and the unsolved Hecke orbit conjecture for unitary Shimura varieties. This action is called the Lubin-Tate action. We first show sufficient conditions for geometrically modelling...
A great deal of work has been done in recent years to construct algebraic invariants ofLegendrian knots, and their higher-dimensional analogues. Here we employ the diagram-
matic calculus developed in [3], in order to develop an iterative method for computing the
so-called vexillary functions of a class of Legendrian surfaces....
Neisseria gonorrhoeae (Ng), a strict human pathogen, is the sole causative agent of gonorrhea. Gc possess a complex gene conversion system, the pilin antigenic variation system, (pilin Av), which alters the DNA sequence of the major pilin, PilE. Pilin Av results in the constant alteration of the surface exposed appendage,...
This dissertation consists of three chapters that each study the interaction between government policy and real estate markets. All three chapters are connected by a broad interest in renters, landlords, and rental markets. Chapter 1 investigates the relationship between place-based policies and real estate and rental markets empirically by studying...
Arising from the study of multiple ergodic averages, nilsequences and multiple correlation sequences lie at the crossroads of ergodic theory, combinatorics and number theory. We study these types of sequences along various subsequences of integers, and provide applications to ergodic theory and harmonic analysis. Our first result involves multiple correlation...
Chapter 1 presents analysis comparing the effectiveness of two mechanisms of regulation enforcement: (1) the frequency of inspections and (2) penalties for violations. Recent policy changes regarding enforcement of mining safety regulations are exploited to quantify the effectiveness of each mechanism. It is concluded that increasing the frequency of inspections...
Photochemistry is an inherently interdiscplinary field where very large energies are leveraged for the making and breaking of bonds. My work has broadly dealt with various strategies to control how energy delivered by light can be channeled into useful functions. I developed a strategy to control the chemo- and stereo-selectivity...