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Optimization Methods For Tabular Data Protection, Iryna Petrenko
Optimization Methods For Tabular Data Protection, Iryna Petrenko
Electronic Theses and Dissertations
In this thesis we consider a minimum distance Controlled Tabular Adjustment (CTA) model for statistical disclosure limitation (control) of tabular data. The goal of the CTA model is to find the closest safe table to some original tabular data set that contains sensitive information. The measure of closeness is usually measured using l1 or l2 norm; with each measure having its advantages and disadvantages. According to the given norm CTA can be formulated as an optimization problem: Liner Programing (LP) for l1, Quadratic Programing (QP) for l2. In this thesis we present an alternative …
A Quantum Astrochemical Perspective On The C-C3h Radical With Application To The Interstellar Medium, Matthew Bassett
A Quantum Astrochemical Perspective On The C-C3h Radical With Application To The Interstellar Medium, Matthew Bassett
Electronic Theses and Dissertations
The interstellar medium (ISM) has been an area of focus for astrochemists and quantum chemists for many years, with particular interest in the presence of interstellar molecules and the resulting chemical processes. The c-C3H radical has been detected in the ISM near the dark molecular cloud TMC-1. With the application of ab initio computational methods using coupled-cluster theory at the singles, doubles, and perturbative triples [CCSD(T)] level, highly accurate quartic force fields (QFFs) are constructed to define the electronic wavefunction for the inter nuclear Hamiltonian. The QFF is used to predict the equilibrium geometry and produce vibrational frequencies, rotational constants, …
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Dynamics Of Gene Networks In Cancer Research, Paul Scott
Electronic Theses and Dissertations
Cancer prevention treatments are being researched to see if an optimized treatment schedule would decrease the likelihood of a person being diagnosed with cancer. To do this we are looking at genes involved in the cell cycle and how they interact with one another. Through each gene expression during the life of a normal cell we get an understanding of the gene interactions and test these against those of a cancerous cell. First we construct a simplified network model of the normal gene network. Once we have this model we translate it into a transition matrix and force changes on …
A Journey To Fuzzy Rings, Brett T. Ernst
A Journey To Fuzzy Rings, Brett T. Ernst
Electronic Theses and Dissertations
Enumerative geometry is a very old branch of algebraic geometry. In this thesis, we will describe several classical problems in enumerative geometry and their solutions in order to motivate the introduction of tropical geometry. Finally, fuzzy rings, a powerful algebraic framework for tropical and algebraic geometry is introduced.
Fiber Products In Commutative Algebra, Keller Vandebogert
Fiber Products In Commutative Algebra, Keller Vandebogert
Electronic Theses and Dissertations
The purpose of this thesis is to introduce and illustrate some of the deep connections between commutative and homological algebra. We shall cover some of the fundamental definitions and introduce several important classes of commutative rings. The later chapters will consider a particular class of rings, the \emph{fiber product}, and, among other results, show that any Gorenstein fiber product is precisely a one dimensional hypersurface. It will also be shown that any Noetherian local ring with a (nontrivially) decomposable maximal ideal satisfies the Auslander-Reiten conjecture. To conclude, generalizations of results by Takahashi and Atkins-Vraciu shall be presented.
Pattern Containment In Circular Permutations, Charles Lanning
Pattern Containment In Circular Permutations, Charles Lanning
Electronic Theses and Dissertations
Pattern containment in permutations, as opposed to pattern avoidance, involves two aspects. The first is to contain every pattern at least once from a given set, known as finding superpatterns; while the second is to contain some given pattern as many times as possible, known as pattern packing. In this thesis, we explore these two questions in circular permutations and present some interesting observations. We also raise some questions and propose some directions for future study.
Graph Invariants Of Trees With Given Degree Sequence, Rachel Bass
Graph Invariants Of Trees With Given Degree Sequence, Rachel Bass
Electronic Theses and Dissertations
Graph invariants are functions defined on the graph structures that stay the same under taking graph isomorphisms. Many such graph invariants, including some commonly used graph indices in Chemical Graph Theory, are defined on vertex degrees and distances between vertices. We explore generalizations of such graph indices and the corresponding extremal problems in trees. We will also briefly mention the applications of our results.
Combinatorics Of Compositions, Meghann M. Gibson
Combinatorics Of Compositions, Meghann M. Gibson
Electronic Theses and Dissertations
Integer compositions and related enumeration problems have been extensively studied. The cyclic analogues of such questions, however, have significantly fewer results. In this thesis, we follow the cyclic construction of Flajolet and Soria to obtain generating functions for cyclic compositions and n-color cyclic compositions with various restrictions. With these generating functions we present some statistics and asymptotic formulas for the number of compositions and parts in such compositions. Combinatorial explanations are also provided for many of the enumerative observations presented.