Dissertations and Theses  Mathematics, Statistics, and Computer Science
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An Analysis of Multivariate FinalOffer Arbitration
(20160908)When negotiations fail, arbitration is often an effective means by which a binding resolution can be found. To address the many shortcomings of conventional arbitration, many industries have been using a variation called ... 
The Effective Cone of Moduli Spaces of Sheaves on a Smooth Quadric Surface
(20161019)In this paper, we provide an approach to computing the effective cone of moduli spaces of sheaves on a smooth quadric surface. We find BrillNoether divisors spanning extremal rays of the effective cone using resolutions ... 
Model Theory and Extremal Combinatorics: Structure, Enumeration, and 01 Laws
(20161019)This thesis investigates connections between model theory and extremal combinatorics. The first part of the thesis consists of an analysis of discrete metric spaces and multigraphs, from the point of view of extremal ... 
Compact Structures in Descriptive Classification Theory
(20161019)An equivalence relation, E, on a Polish topological space, X, is Borel reducible to another, F, on Y, when there is a Borelmeasurable function from X to Y assigning Fclasses as complete invariants for E. Descriptive ... 
Studies on Some Inferential Aspects of GraybillDeal Estimators
(20161019)This dissertation included two elds in the application of Statistical Inference, specialized in Meta Analysis and Estimation Theory viz. : `Estimation of Common Mean' and `function Estimation'. Part A Estimation of Common ... 
Optimal Biomarkerstratified Design and Adaptive Design in Mixture Distributions
(20161019)In the first part of this dissertation, an optimal design for precision medicine is introduced. Different patients could respond differently to the same drug, and the ineffective rate of a particular drug could be quite ... 
Singular Loci of Restriction Varieties
(20161019)Restriction varieties in the orthogonal Grassmannian are subvarieties of OG(k, n) defined by rank conditions given by a flag that is not necessarily isotropic with respect to the relevant symmetric bilinear form. In ... 
Logarithmic Potentials and Quasiconformal Flows on the Heisenberg Group
(20161019)In a first contribution to the quasiconformal Jacobian problem outside the Euclidean setting, we show that if the total variation of the measure associated to a quasilogarithmic potential on the Heisenberg group is ... 
Ergodic Theory and Geometry of Nilpotent Groups
(20161018)We investigate the ergodic theory and geometry of finitely generated virtually nilpotent groups. Let Γ be a finitely generated virtually nilpotent group. In the first part of the thesis, we consider three closely related ... 
Topics in Knowledge Representation: Belief Revision and Conditional Knowledge Bases
(20161018)Results in two topics within knowledge representation and reasoning are presented. The first, belief revision, concentrates on incorporation of new knowledge into previous knowledge. The objective of research presented ... 
The Hilbert Schemes of Points on Singular Varieties and Kodaira NonVanishing in Characteristic p
(20161018)The thesis consists of two parts of work. In the first part, we study the geometry of the Hilbert schemes of points on singular curves and surfaces. In particular, the Hilbert scheme is irreducible for a surface with only ... 
Problems of Regularity in Models Arising from Fluid Dynamics
(20161018)This work expands regularity results for equations related to fluid motion. First, we improve previously known lower bounds for Sobolev norms of potential blowup solutions to the threedimensional NavierStokes equations ... 
Graphs, New Models, and Complexity
(20160701)Over the past few decades the internet and social networks became central to our society. As a consequence, the study of networks and the algorithmic complexity of problems about networks are an increasingly important ... 
On the Law of Iterated Logarithms for Brownian Motion on Compact Manifolds
(20160701)Let M be a compact and smooth Riemannian manifold. Take a Brownian motion on the manifold. We take a family of measures defined by the Law of Iterated Logarithms for Brownian Motions on Compact Manifolds, as in Brosamler ... 
DataIntensive Remote Collaboration using Scalable Visualizations in Heterogeneous Display Spaces
(20160701)Commercial software, such as Google Hangouts, Skype, and WebEx, has made significant strides to enhance remote collaboration between single users. Other systems, such as Oblong’s Mezzanine, have enabled groups to collaborate ... 
Multiagent Stochastic Planning with Bayesian Policy Recognition
(20160701)We consider an autonomous agent facing a stochastic, partially observable, multiagent environment. In order to compute an optimal plan, the agent must accurately predict the actions of the other agents, since they influence ... 
Information Networks: Problems, Theories and Applications
(20160701)Nowadays, online information networks widely exist in our daily lives. The flourishing of various types of information networks have raised numerous challenging problems, as well as innovative applications. This dissertation ... 
Diagrammatic Theories of 1 and 2 Dimensional Knots
(20160701)A metatheory is described whereby any diagrammatic knot theory may be defined by specifying diagrams and moves. This is done explicitly in dimensions 1 and 2, with more abstract indication of how to extend the metatheory ... 
On The Structured Manifold Optimization: Reducedrank and Positive Definite Matrix Estimation
(20160217)This thesis mainly proposes optimization schemes regarding both types of structured matrices, as well as their applications in statistics. The first structured matrix optimization is proposed under the reducedrank ... 
Dynamics of Equicontinuous Group Actions on Cantor Sets
(20160216)In this thesis, we consider the class of minimal equicontinuous Cantor dynamical systems. We show that every such system can be represented by a group chain inverse limit system, and conversely that every group chain yeilds ...