Mathematics
Recent Submissions

Joint shape and motion estimation from echobased sensor data
Given a set of timeseries data collected from echobased ranging sensors, we study the problem of jointly estimating the shape and motion of the target under observation when the sensor positions are also unknown. Using ... 
FDOAbased passive source localization : a geometric perspective
We consider the problem of passively locating the source of a radiofrequency signal using observations by several sensors. Received signals can be compared to obtain time difference of arrival (TDOA) and frequency difference ... 
Functional programming applied to computational algebra
Underlying many, if not all, areas of mathematics is category theory, an alternative to set theory as a foundation that formalizes mathematical structures and relations between them. These relations abstract the idea of a ... 
Bayesian approach to the anisotropic EIT problem and effect of structural changes on reconstruction algorithm using 2D Dbar algorithm
Electrical Impedance Tomography (EIT) is a relatively new imaging technique that is noninvasive, lowcost, and nonionizing with excellent temporal resolution.In EIT, the unknown electrical conductivity in the interior ... 
Elevation heterogeneity and the spread of Whitenose syndrome in bats
Whitenose syndrome (WNS) has been decimating bat populations throughout North America since its discovery in New York during the winter of 20062007. The fungus responsible for the disease, Pseudogymnoascus destructans, ... 
Intersections of ψ classes on Hassett spaces of rational curves
Hassett spaces are moduli spaces of weighted stable pointed curves. In this work, we consider such spaces of curves of genus 0 with weights all 1/q , q being a positive integer greater than or equal to 2. These spaces are ... 
Group extensions problem and its resolution in cohomology for the case of an elementary abelian normal subgroup, The
The JordanHölder theorem gives a way to deconstruct a group into smaller groups, The converse problem is the construction of group extensions, that is to construct a group G from two groups Q and K where K ≤ G and G/K ≅ ... 
Covariance integral invariants of embedded Riemannian manifolds for Manifold Learning
This thesis develops an effective theoretical foundation for the integral invariant approach to study submanifold geometry via the statistics of the underlying pointset, i.e., Manifold Learning from covariance analysis. ... 
Asymptotic enumeration of matrix groups
We prove that the general linear group GLd(pe) has between pd4e/64O(d2) and pd4e2·log2p distinct isomorphism types of subgroups. The upper bound is obtained by elementary counting methods, where as the lower bound is found ... 
Synthetic Aperture Source Localization
The detection and localization of sources of electromagnetic (EM) radiation has many applications in both civilian and defense communities. The goal of source localization is to identify the geographic position of an emitter ... 
Commutative algebra in the graded category with applications to equivariant cohomology rings
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Weak Galerkin finite element methods for the Darcy equation
The Darcy equation models pressuredriven flow in porous media. Because of the importance of ground water flow in oil recovery and waste mitigation, several types of numerical methods have been developed for solving the ... 
Numerical algebraic geometry approach to polynomial optimization, The
Numerical algebraic geometry (NAG) consists of a collection of numerical algorithms, based on homotopy continuation, to approximate the solution sets of systems of polynomial equations arising from applications in science ... 
Topological techniques for characterization of patterns in differential equations
Complex data can be challenging to untangle. Recent advances in computing capabilities has allowed for practical application of tools from algebraic topology, which have proven to be useful for qualitative and quantitative ... 
First year graduate teaching assistants : fostering successful teaching
The importance of effective graduate teaching assistant (GTA) training is often greatly under appreciated. However, it is imperative that GTAs receive optimal professional development because they are often responsible for ... 
Pattern formation in reaction diffusion systems and ion bombardment of surfaces
We have analyzed pattern formation in two different systems: (1) Vaportoparticle reaction diffusion systems and (2) Highly ordered square arrays in ion bombardment. The vaportoparticle reaction exhibits oscillatory ... 
Geometric data analysis approach to dimension reduction in machine learning and data mining in medical and biological sensing, A
Geometric data analysis seeks to uncover and leverage structure in data for tasks in machine learning when data is visualized as points in some dimensional, abstract space. This dissertation considers data which is high ... 
On automorphism groups of pgroups
We provide the necessary framework to use filters in computational settings, in particular for finitely generated nilpotent groups. The main motivation for this is to construct automorphisms of the group from derivations ... 
Grassmann, Flag, and Schubert varieties in applications
This dissertation develops mathematical tools for signal processing and pattern recognition tasks where data with the same identity is assumed to vary linearly. We build on the growing canon of techniques for analyzing and ... 
Avoiding singularities during homotopy continuation
In numerical algebraic geometry, the goal is to find solutions to a polynomial system F(x1,x2,...xn). This is done through a process called homotopy continuation. During this process, it is possible to encounter areas of ...