We consider join congruence relations on geometric lattices from three different points of view. First, recognizing that every matroid has an associated geometric lattice, we consider matroid operations and give conditions for when it is possible...
Movies; Craig Blake (Jeff Bridges) and Mary Tate (Sally Field) consider their relationship in "Stay Hungry", a United Artists release. Copyright 1976; United Artists Corporation; all rights reserved; printed in U.S.A.; "Stay Hungry", a movie...
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...
Internet -- Security measures. Public key infrastructure (Computer security). Digital signatures. Peer-to-peer architecture (Computer networks) -- Security measures.
The Internet has become a virtual place where people not only operate in isolation but also interact with other Internet users. Collaborative systems are becoming more popular. Applications now being introduced could provide better remote education...
The BCL2 family of proteins control intrinsic apoptosis at the mitochondria through a delicate balance of pro and anti-apoptotic proteins. Anti-apoptotic proteins are frequently relied upon by cancer cells, making them ideal targets for...
The auroral zone is a rich source of natural radio emissions that can be observed in space and at ground-level. By studying these waves, scientists can gain insight into the plasma processes that generate them and use the near-Earth space...
Molecular imaging of cancer features is a critical part of advancing better tools for oncology management and drug discovery, yet it is still evolving as a useful tool. Diffuse Fluorescence Tomography (FT) is one approach to molecular imaging, used...
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...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
Anabolic-androgenic steroids (AAS) are synthetic derivatives of the gonadal hormone, testosterone. Despite their many untoward side effects, AAS are wildly abused for their ergogenic properties. AAS have numerous effects on many organ systems,...
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...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
This thesis investigates a notion of Turing reducibility introduced by Winkler [8] that is total on all computably enumerable oracles. Groszek and Weber show in [7] that this is a new notion of reducibility and it is not transitive. They give su...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
Vibrio cholerae is a gram-negative bacterial pathogen that causes the severe diarrheal disease cholera. Several bacterial factors have been identified that are critical for V. cholerae intestinal colonization. The best characterized of these...
An investigation of the mechanical properties of Fe-Al single crystals by tensile testing both at different strain rates (10 -7 s -1 to 1 s -1 ) and in different environments (air, vacuum, or oxygen), showed that moisture-produced hydrogen in Fe-Al...