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...
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...
Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
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...
'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate...
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...
Electronic data processing -- Distributed processing. ; Computer network architectures. ; Programming languages (Electronic computers) -- Semantics. ; Database management.
I tackle the problem of naming and sharing resources across administrative boundaries. Conventional systems manifest the hierarchy of typical administrative structure in the structure of their own mechanism. While natural for communication that...
An interval order is an ordered set whose elements are in correspondence with a collection of intervals in a linearly ordered set, with disjoint intervals ordered by their relative position. The order complex of an ordered set is the simplicial...
This thesis presents technologies for the design, fabrication, operation, and control of electrostatic MEMS micro-robots. It describes prototype micro-robots, with dimensions of 60 Î¼m by 250 Î¼m by 10 Î¼m, that are capable of controllable...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
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...
Recent years have witnessed a new class of monitoring applications that need to continuously collect information from remote data sources. Those data sources, such as web click-streams, stock quotes, and sensor data, are often characterized as...
PDZ protein-protein interaction domains recognize short linear motif (SLiM) sequences typically at the extreme C-terminus of a target protein. These domains often act as scaffolds, connecting target proteins to additional interaction and catalytic...
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...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Proteins are ubiquitous in cells and are essential to a wide range of biological processes. Since existing proteins occupy only a small portion of the space of possible amino acid composition, understanding their sequence-structure-function...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...