Now showing items 1-20 of 350

    • Statistical Inference for Large Matrices 

      Xia, Dong (Georgia Institute of Technology, 2016-07-29)
      This thesis covers two topics on matrix analysis and estimation in machine learning and statistics. The first topic is about density matrix estimation with application in quantum state tomography. The density matrices are ...
    • Open book decompositions in high dimensional contact manifolds 

      Elmas, Gokhan (Georgia Institute of Technology, 2016-05-27)
      In this thesis, we study the open book decompositions in high dimensional contact manifolds. We focus on the results about open book decomposition of manifolds and their relationship with contact geometry.
    • Transverse Surgery on Knots in Contact Three-Manifolds 

      Conway, James (Georgia Institute of Technology, 2016-05-19)
      We study the effect of surgery on transverse knots in contact $3$-manifolds by examining its effect on open books, the Heegaard Floer contact invariant, and tightness in general. We first compare surgery on transverse ...
    • A study of stochastic differential equations and Fokker-Planck equations with applications 

      Li, Wuchen (Georgia Institute of Technology, 2016-04-15)
      Fokker-Planck equations, along with stochastic differential equations, play vital roles in physics, population modeling, game theory and optimization (finite or infinite dimensional). In this thesis, we study three topics, ...
    • The Filippov moments solution on the intersection of two and three manifolds 

      Difonzo, Fabio Vito (Georgia Institute of Technology, 2015-11-18)
      In this thesis, we study the Filippov moments solution for differential equations with discontinuous right-hand side. In particular, our aim is to define a suitable Filippov sliding vector field on a co-dimension $2$ ...
    • Thermostated Kac models 

      Vaidyanathan, Ranjini (Georgia Institute of Technology, 2015-11-16)
      We consider a model of N particles interacting through a Kac-style collision process, with m particles among them interacting, in addition, with a thermostat. When m = N, we show exponential approach to the equilibrium ...
    • Combinatorial problems for graphs and partially ordered sets 

      Wang, Ruidong (Georgia Institute of Technology, 2015-11-13)
      This dissertation has three principal components. The first component is about the connections between the dimension of posets and the size of matchings in comparability and incomparability graphs. In 1951, Hiraguchi proved ...
    • Symmetric ideals and numerical primary decomposition 

      Krone, Robert Carlton (Georgia Institute of Technology, 2015-07-27)
      The thesis considers two distinct strategies for algebraic computation with polynomials in high dimension. The first concerns ideals and varieties with symmetry, which often arise in applications from areas such as algebraic ...
    • Multifold sums and products over R, and combinatorial problems on sumsets 

      Bush, Albert (Georgia Institute of Technology, 2015-07-22)
      We prove a new bound on a version of the sum-product problem studied by Chang. By introducing several combinatorial tools, this expands upon a method of Croot and Hart which used the Tarry-Escott problem to build distinct ...
    • Minimization problems involving polyconvex integrands 

      Awi, Romeo Olivier (Georgia Institute of Technology, 2015-06-02)
      This thesis is mainly concerned with problems in the areas of the Calculus of Variations and Partial Differential Equations (PDEs). The properties of the functional to minimize with respect to the given topology play an ...
    • Complete nonnegatively curved spheres and planes 

      Hu, Jing (Georgia Institute of Technology, 2015-06-02)
      We study the space of complete Riemannian metrics of nonnegative curvature on the sphere equipped with C^{k+\alpha} topology. We show the space is homogenous for k>=2. If k is infinite, we show that the space is homeomorphic ...
    • Small-time asymptotics of call prices and implied volatilities for exponential Lévy models 

      Hoffmeyer, Allen Kyle (Georgia Institute of Technology, 2015-01-08)
      We derive at-the-money call-price and implied volatility asymptotic expansions in time to maturity for a selection of exponential Lévy models, restricting our attention to asset-price models whose log returns structure is ...
    • Numerical algorithms based on the back and forth error compensation and correction 

      Hu, Lili (Georgia Institute of Technology, 2014-12-18)
      In this thesis we carry out a further study of the back and forth error compensation and correction (BFECC) method. The first part discusses the time reversibility of numerical schemes. Motivated by the BFECC method, a ...
    • Some results on sums and products 

      Pryby, Christopher Ian (Georgia Institute of Technology, 2014-11-17)
      We demonstrate new results in additive combinatorics, including a proof of a conjecture by J. Solymosi: for every epsilon > 0, there exists delta > 0 such that, given n² points in a grid formation in R², if L is a set of ...
    • Accelerated algorithms for composite saddle-point problems and applications 

      He, Yunlong (Georgia Institute of Technology, 2014-11-13)
      This dissertation considers the composite saddle-point (CSP) problem which is motivated by real-world applications in the areas of machine learning and image processing. Two new accelerated algorithms for solving composite ...
    • A non-asymptotic study of low-rank estimation of smooth kernels on graphs 

      Rangel Walteros, Pedro Andres (Georgia Institute of Technology, 2014-07-23)
      This dissertation investigates the problem of estimating a kernel over a large graph based on a sample of noisy observations of linear measurements of the kernel. We are interested in solving this estimation problem in the ...
    • Linear systems on metric graphs and some applications to tropical geometry and non-archimedean geometry 

      Luo, Ye (Georgia Institute of Technology, 2014-07-02)
      The divisor theories on finite graphs and metric graphs were introduced systematically as analogues to the divisor theory on algebraic curves, and all these theories are deeply connected to each other via tropical geometry ...
    • A numerical study of vorticity-enhanced heat transfer 

      Wang, Xiaolin (Georgia Institute of Technology, 2014-06-26)
      In this work, we have numerically studied the effect of the vorticity on the enhancement of heat transfer in a channel flow. In the first part of the work, we focus on the investigation of a channel flow with a vortex ...
    • Stein fillings of contact structures supported by planar open books 

      Kaloti, Amey (Georgia Institute of Technology, 2014-06-20)
      In this thesis we study topology of symplectic fillings of contact manifolds supported by planar open books. We obtain results regarding geography of the symplectic fillings of these contact manifolds. Specifically, we ...
    • Invariant densities for dynamical systems with random switching 

      Hurth, Tobias (Georgia Institute of Technology, 2014-06-19)
      We studied invariant measures and invariant densities for dynamical systems with random switching (switching systems, in short). These switching systems can be described by a two-component Markov process whose first component ...