Physical Sciences and Mathematics Commons^™

Free Resolutions Associated To Representable Matroids, Nicholas D. Armenoff

Theses and Dissertations--Mathematics

As a matroid is naturally a simplicial complex, one can study its combinatorial properties via the associated Stanley-Reisner ideal and its corresponding free resolution. Using results by Johnsen and Verdure, we prove that a matroid is the dual to a perfect matroid design if and only if its corresponding Stanley-Reisner ideal has a pure free resolution, and, motivated by applications to their generalized Hamming weights, characterize free resolutions corresponding to the vector matroids of the parity check matrices of Reed-Solomon codes and certain BCH codes. Furthermore, using an inductive mapping cone argument, we construct a cellular resolution for the matroid …

Unimodality Questions In Ehrhart Theory, Robert Davis

Theses and Dissertations--Mathematics

An interesting open problem in Ehrhart theory is to classify those lattice polytopes having a unimodal h^*-vector.Although various sufficient conditions have been found, necessary conditions remain a challenge. Highly-structured polytopes, such as the polytope of real doubly-stochastic matrices, have been proven to possess unimodal h^*-vectors, but the same is unknown even for small variations of it.

In this dissertation, we mainly consider two particular classes of polytopes: reflexive simplices and the polytope of symmetric real doubly-stochastic matrices. For the first class, we discuss an operation that preserves reflexivity, integral closure, and unimodality of the h^{* …}

Determinantal Ideals From Symmetrized Skew Tableaux, Bill Robinson

Theses and Dissertations--Mathematics

We study a class of determinantal ideals called skew tableau ideals, which are generated by t x t minors in a subset of a symmetric matrix of indeterminates. The initial ideals have been studied in the 2 x 2 case by Corso, Nagel, Petrovic and Yuen. Using liaison techniques, we have extended their results to include the original determinantal ideals in the 2 x 2 case, as well as special cases of the ideals in the t x t case. In particular, for any skew tableau ideal of this form, we have defined an elementary biliaison between it and one …

The Krylov Subspace Methods For The Computation Of Matrix Exponentials, Hao Wang

Theses and Dissertations--Mathematics

The problem of computing the matrix exponential e^tA arises in many theoretical and practical problems. Many methods have been developed to accurately and efficiently compute this matrix function or its product with a vector, i.e., e^tAv. In the past few decades, with the increasing need of the computation for large sparse matrices, iterative methods such as the Krylov subspace methods have proved to be a powerful class of methods in dealing with many linear algebra problems. The Krylov subspace methods have been introduced for computing matrix exponentials by Gallopoulos and Saad, and the corresponding error bounds …

Polyhedral Problems In Combinatorial Convex Geometry, Liam Solus

Theses and Dissertations--Mathematics

In this dissertation, we exhibit two instances of polyhedra in combinatorial convex geometry. The first instance arises in the context of Ehrhart theory, and the polyhedra are the central objects of study. The second instance arises in algebraic statistics, and the polyhedra act as a conduit through which we study a nonpolyhedral problem.

In the first case, we examine combinatorial and algebraic properties of the Ehrhart h*-polynomial of the r-stable (n,k)-hypersimplices. These are a family of polytopes which form a nested chain of subpolytopes within the (n,k)-hypersimplex. We show that a well-studied unimodular triangulation of the (n,k)-hypersimplex restricts to a …

Design, Synthesis, And Pharmacological Evaluation Of Three Series Of Lobelane Analogs As Inhibitors Of The Vesicular Monoamine Transporter (Vmat2), John P. Culver

Theses and Dissertations--Pharmacy

Methamphetamine (METH) abuse is a serious problem in the United States and worldwide. The reward experienced by METH users is due to the increase in extracellular dopamine (DA) concentrations caused by an interaction between METH and the DA transporter (DAT) as well as the Vesicular Monoamine Transporter-2 (VMAT2). The reward felt by users of METH leads to further use of the drug and subsequent abuse. The current project examined the ability of three novel series of lobelane analogs to interact with a binding site on the Vesicular Monoamine Transporter-2 (VMAT2) in an attempt to inhibit the effects of METH. Lobelane …

A Molecular-Level View Of The Physical Stability Of Amorphous Solid Dispersions, Xiaoda Yuan

Theses and Dissertations--Pharmacy

Many pharmaceutical compounds being developed in recent years are poorly soluble in water. This has led to insufficient oral bioavailability of many compounds in vitro. The amorphous formulation is one of the promising techniques to increase the oral bioavailability of these poorly water-soluble compounds. However, an amorphous drug substance is inherently unstable because it is a high energy form. In order to increase the physical stability, the amorphous drug is often formulated with a suitable polymer to form an amorphous solid dispersion. Previous research has suggested that the formation of an intimately mixed drug-polymer mixture contributes to the stabilization …

The Host Galaxies Of X-Ray Selected Active Galactic Nuclei To Z = 2.5: Structure, Star Formation, And Their Relationships From Candels And Herschel/Pacs, Dale D. Kocevski, D. J. Rosario, D. H. Mcintosh, A. Van Der Wel, J. Kartaltepe, P. Lang, P. Santini, S. Wuyts, D. Lutz, M. Rafelski, C. Villforth

Physics and Astronomy Faculty Publications

We study the relationship between the structure and star formation rate (SFR) of X-ray selected low and moderate luminosity active galactic nuclei (AGNs) in the two Chandra Deep Fields, using Hubble Space Telescope imaging from the Cosmic Assembly Near Infrared Extragalactic Legacy Survey (CANDELS) and deep far-infrared maps from the PEP+GOODS-Herschel survey. We derive detailed distributions of structural parameters and FIR luminosities from carefully constructed control samples of galaxies, which we then compare to those of the AGNs. At z ~ 1, AGNs show slightly diskier light profiles than massive inactive (non-AGN) galaxies, as well as modestly higher levels …

Kentucky Water Resources Research Institute Annual Technical Report Fy 2014, Kentucky Water Resources Research Institute, University Of Kentucky

KWRRI Annual Technical Reports (USGS’s 104b Grant Program)

The 2014 Annual Technical Report for Kentucky consolidates reporting requirements for the Section 104(b) base grant award into a single document that includes: 1) a synopsis of each research project that was conducted during the period, 2) citations for related publications, reports, and presentations, 3) a description of information transfer activities, 4) a summary a student support during the reporting period, and 5) notable awards and achievements during the year.

Empirical Likelihood Confidence Band, Shihong Zhu

Theses and Dissertations--Statistics

The confidence band represents an important measure of uncertainty associated with a functional estimator and empirical likelihood method has been proved to be a viable approach to constructing confidence bands in many cases. Using the empirical likelihood ratio principle, this dissertation developed simultaneous confidence bands for many functions of fundamental importance in survival analysis, including the survival function, the difference and ratio of survival functions, the hazards ratio function, and other parameters involving residual lifetimes. Covariate adjustment was incorporated under the proportional hazards assumption. The proposed method can be very useful when, for example, an individualized survival function is desired …

New Results In Ell_1 Penalized Regression, Edward A. Roualdes

Theses and Dissertations--Statistics

Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the …