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 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...
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...
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...
In the past few years there has been a tremendous growth in the usage of digital images. Users can now access millions of photos, a fact that poses the need of having methods that can efficiently and effectively search the visual information of...
Information retrieval -- Mathematical models. ; Electronic information resource searching. ; Computer algorithms. ; Decision making -- Data processing. ; Mathematical optimization.
This thesis presents a unified method for simultaneous solution of three problems in Information Retrieval--metasearch (the fusion of ranked lists returned by retrieval systems to elicit improved performance), efficient system evaluation (the...
Sponges are a historically ambiguous taxon, often considered primitively simple representatives of early Metazoa, living fossils from the era before the complex morphological features of the bilaterian phyla appeared in the Cambrian. Yet recent...
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...
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...
Spectral theory is the subfield of differential geometry which provided the solution to Kac''s famous question, "Can you hear the shape of a drum?" That is, can we use the Laplace spectrum of a manifold to draw conclusions about its geometry or...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...