This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of the...
Magnetic nanoparticles are promising candidates for use in biomedical applications as remote sensors of biophysical properties, thermal therapy agents, and detectors of specific biomolecules. Many approaches have been used to model magnetic...
During our fieldwork with real-world organizations---including those in Public Key Infrastructure (PKI), network configuration management, and the electrical power grid---we repeatedly noticed that security policies and related security artifacts...
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...
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...
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...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...
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...
Prion diseases are fatal neurodegenerative disorders which affect a variety of different animal species including humans. The central pathogenic event underlying prion diseases is the conformational conversion of the cellular prion protein (PrP C )...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
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...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
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...
In this thesis data from four sounding rocket experiments (PHAZE II, SIERRA, RACE and HIBAR) are used to explore the high and medium frequency waves seen in the auroral ionosphere. All rockets were launched into active aurora and carried both...
Prion diseases are infectious neurodegenerative disorders characterized by a conformational change of the host-encoded prion protein. The normal nonpathogenic isoform of the prion protein (PrPc) is primarily composed of α-helices and very low...
The thesis is devoted to the effects of electromagnetic coupling between the Earth's magnetosphere and the active auroral ionosphere. The research has been focused, in particular, on the concept of ionospheric feedback instability. The feedback...
The study of twin primes gives rise to several famously difficult problems in number theory--in fact, we still cannot definitively say whether there are infinitely many twin primes. In this work, we consider a related problem, namely: What is the...
Topological graph theory. Aperiodicity. Paths and cycles (Graph theory)
The condition ""every cycle has an entry"" first appeared in the literature in Kumjian, Pask, and Raeburn's paper on Cuntz-Krieger algebras of directed graphs, where it was called Condition (L). It provides a necessary condition for simplicity of...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
Football Fifth Down Game (Cornell); cartoon about the 5th down in the Dartmouth-Cornell game: "We got to checking our records after the game... ...and we followed things all right till... things got out of hand, but Bill Murphy soon put a stop to...