Now showing items 1-10 of 102
- . . .
Möbius number of the symmetric group, The
Contributor:Monks, Kenneth M.
The Möbius number of a finite group is its most important nontrivial combinatorial invariant. In this paper, we compute the Möbius numbers of many partially-ordered sets, including the odd-partition posets and the subgroup ...
Computer vision approach to classification of circulating tumor cells
Current research into the detection and characterization of circulating tumor cells (CTCs) in the bloodstream can be used to assess the threat to a potential cancer victim. We have determined specific goals to further the ...
Posteriori error estimates for the Poisson Problem on closed, two-dimensional surfaces, A
Contributor:Newton, William F.
The solution of partial differential equations on non-Euclidean Domains is an area of much research in recent years. The Poisson Problem is a partial differential equation that is useful on curved surfaces. On a curved ...
Mean variants on matrix manifolds
Contributor:Marks, Justin D.
The geometrically elegant Stiefel and Grassmann manifolds have become organizational tools for data applications, such as illumination spaces for faces in digital photography. Modern data analysis involves increasingly ...
Exploiting geometry, topology, and optimization for knowledge discovery in big data
Contributor:Ziegelmeier, Lori Beth
In this dissertation, we consider several topics that are united by the theme of topological and geometric data analysis. First, we consider an application in landscape ecology using a well-known vector quantization algorithm ...
Conjugacy classes of matrix groups over local rings and an application to the enumeration of abelian varieties
Contributor:Williams, Cassandra L.
The Frobenius endomorphism of an abelian variety over a finite field Fq of dimension g can be considered as an element of the finite matrix group GSp2g(Z/lr). The characteristic polynomial of such a matrix defines a union ...
Computational advancements in the D-bar reconstruction method for 2-D electrical impedance tomography
We study the problem of reconstructing 2-D conductivities from boundary voltage and current density measurements, also known as the electrical impedance tomography (EIT) problem, using the D-bar inversion method, based on ...
Sparse multivariate analyses via ℓ1-regularized optimization problems solved with Bregman Iterative Techniques
In this dissertation we propose Split Bregman algorithms for several multivariate analytic techniques for dimensionality reduction and feature selection including Sparse Principal Components Analysis, Bisparse Singular ...
Sensitivity analysis of the basic reproduction number and other quantities for infectious disease models
Contributor:Mikucki, Michael A.
Performing forward sensitivity analysis has been an integral component of mathematical modeling, yet its implementation becomes increasingly difficult with a model's complexity. For infectious disease models in particular, ...
Preconditioning Polynomial Systems Using Macaulay Dual Spaces
Contributor:Ihde, Steven L.
Polynomial systems arise in many applications across a diverse landscape of subjects. Solving these systems has been an area of intense research for many years. Methods for solving these systems numerically fit into the ...