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Multidimensional Toggle Dynamics
(North Dakota State University, 2018)
J. Propp and T. Roby isolated a phenomenon in which a statistic on a set has the same average value over any orbit as its global average, naming it homomesy. One set they investigated was order ideals of partially ordered ...
Some Results on Semicrossed Products and Related Operator Algebras
(North Dakota State University, 2021)
We investigate various properties of two classes of operator algebras: directed graph operator algebras and semicrossed products. First we consider analytic structure in the form of derivations and point derivations on ...
Subfractals Induced by Subshifts
(North Dakota State University, 2016)
In this thesis, a subfractal is the subset of points in the attractor of an iterated function
system in which every point in the subfractal is associated with an allowable word from a subshift
on the underlying symbolic ...
Hypothesis Testing on Time Series Driven by Underlying Lévy Processes, with Machine Learning Applications
(North Dakota State University, 2021)
In this dissertation, we study the testing of hypotheses on streams of observations that are driven by Lévy processes. This is applicable for sequential decision making on the state of two-sensor systems. In one case, each ...
Maximally Edge-Colored Directed Graph Algebras
(North Dakota State University, 2017)
Graph C*-algebras are constructed using projections corresponding to the vertices of the graph, and partial isometries corresponding to the edges of the graph. Here, we use the gauge-invariant uniqueness theorem to first ...
Applications of Groups of Divisibility and a Generalization of Krull Dimension
(North Dakota State University, 2011)
Groups of divisibility have played an important role in commutative algebra for many years. In 1932 Wolfgang Krull showed in [12] that every linearly ordered Abelian group can be realized as the group of divisibility of a ...
Sign Matrix Polytopes
(North Dakota State University, 2018)
Motivated by the study of polytopes formed as the convex hull of permutation matrices and alternating sign matrices, several new families of polytopes are defined as convex hulls of sign matrices, which are certain ...
On Partial Permutations and Alternating Sign Matrices: Bijections and Polytopes
(North Dakota State University, 2021)
Motivated by the study of chained permutations and alternating sign matrices, we investigate partial permutations and alternating sign matrices. We give a length generating function for partial permutations and show ...
Optimization Problems Arising in Stability Analysis of Discrete Time Recurrent Neural Networks
(North Dakota State University, 2016)
We consider the method of Reduction of Dissipativity Domain to prove global Lyapunov
stability of Discrete Time Recurrent Neural Networks. The standard and advanced criteria for
Absolute Stability of these essentially ...
NAK for Ext, Ascent of Module Structures, and the Blindness of Extended Modules
(North Dakota State University, 2012)
This dissertation investigates the interplay between properties of Ext modules and ascent of module structures along ring homomorphisms. First, we consider a flat local ring homomorphism ϕ: (R, [special characters omitted], ...