In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
Magnetic nanoparticle-based hyperthermia for cancer treatment is a promising technology, particularly when applied as part of an adjuvant strategy with established cancer therapies (chemotherapy, radiation and surgery). In Europe, early clinical...
Nanoparticles have made significant advances in recent years in the realm of cancer therapy. These nanoparticles typically range in size from 10-250nm in diameter, allowing for differential systemic-based biodistribution. The enhanced permeability...
The processes affecting gas transport through the firn column are important to understand in order to accurately interpret climate records from ice cores. Historically, density measurements have been used to estimate open and closed porosity in the...
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
Phosphatidylinositol 3-kinase (PI3K) is a major positive regulator of the PI3K signaling pathway that regulates many important cellular functions including growth, proliferation, survival, metabolism, and angiogenesis. The PIK3CA gene, encoding the...
We present aligned hierarchies, a novel solution to the dimension reduction problem, representing high-dimensional and noisy sequential data as a low-dimensional object that encodes relevant information. In this thesis, we motivate our presentation...
Wireless communication systems. Computer network protocols.
We evaluate mobility predictors in wireless networks. Handoff prediction in wireless networks has long been considered as a mechanism to improve the quality of service provided to mobile wireless users. Most prior studies, however, were based on...
Snowmelt from seasonal snow covers can be significant in many environments of northern and alpine areas. Water flow and chemical transport resulting from snowmelt have been studied for an understanding of contributions to watersheds or catchments....
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
Arsenic is implicated in numerous human pathologies, including cancer and several forms of liver disease. One contributing mechanism may involve alterations of CYP levels by arsenic. CYP3As are the most abundant CYP proteins in human liver and...
In the past decade, the use of ordinal patterns in the analysis of time series and dynamical systems has become an important tool. Ordinal patterns (otherwise known as a permutation patterns) are found in time series by taking n data points at...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
I. Markovnikov-Selective Hydrothiolation of Styrenes: Application to the Synthesis of Stereodefined Olefins There have been few reports in the literature describing Lewis Acid-catalyzed hydrothiolations that furnish Markovnikov-selective C–S bond...
Understanding mercury (Hg) and lead (Pb) accumulation and retention in forest soils is needed to reduce their negative impacts on human and wildlife health. In addition, mercury and lead can be used to characterize the role of soil in terrestrial...
Protein secretion is executed by the secretory pathway, which involves the delivery of membrane and soluble secretory proteins in vesicle intermediates that capture newly-synthesized proteins assembled in the endoplasmic reticulum (ER) and then...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
As the human population increases, it is imperative that we develop strategies to improve agricultural productivity to meet the growing demand for food, fuel and fiber. More than 2 billion people suffer from "hidden hunger" (a lack of essential...
Sea ice appears to form an impenetrable boundary at the ocean-atmosphere interface in polar regions, yet in fact its porous structure provides critical pathways for the exchange of heat, gases, salts, and other chemical species impacting the global...
Arctic temperature and precipitation have been rising over recent decades, with implications for Greenland Ice Sheet (GrIS) mass balance, sea level rise, and thermohaline circulation via Arctic Ocean freshening. However, meteorological station data...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...