School of Mathematics Theses and Dissertations
Original work in partial fulfillment of the requirements for a graduate degree from the School of Mathematics.
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Recent Submissions
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Topics on the Longest Common Subsequences: Simulations, Computations, and Variance
(Georgia Institute of Technology, 2018-11-07)The study of the longest common subsequences (LCSs) of two random words/strings is classical in computer science and bioinformatics. A problem of particular probabilistic interest is to determine the limiting behavior of ... -
Statistical Inference for High Dimensional Data with Low Rank Structure
(Georgia Institute of Technology, 2018-10-19)We study two major topics on statistical inference for high dimensional data with low rank structure occurred in many machine learning and statistics applications. The first topic is about nonparametric estimation of low ... -
Non-negative symmetric polynomials and entangled Bosons
(Georgia Institute of Technology, 2018-09-07)The fundamental relation between quantum entanglement and convex algebraic geometry has unveiled a set of powerful tools, imported from the former to the study the latter. The space of separable mixed states is convex and ... -
COMBINATORIAL MODELS FOR SURFACE AND FREE GROUP SYMMETRIES
(Georgia Institute of Technology, 2018-08-15)The curve complex of Harvey allows combinatorial representation of a surface mapping class group by describing its action on simple closed curves. Similar complexes of spheres, free factors, and free splittings allow ... -
The back and forth error compensation and correction method for linear hyperbolic systems and a conservative BFECC limiter
(Georgia Institute of Technology, 2018-07-25)In this thesis, we studied the Back and Forth Error Compensation and Correction (BFECC) method for linear hyperbolic PDE systems and nonlinear scalar conservation laws. We extend the BFECC method from scalar hyperbolic ... -
Dynamics of religious group growth and survival
(Georgia Institute of Technology, 2018-07-23)We model and analyze the dynamics of religious group membership and size. A groups is distinguished by its strictness, which determines how much time group members are expected to spend contributing to the group. Individuals ... -
Geometric bijections of graphs and regular matroids
(Georgia Institute of Technology, 2018-07-31)The Jacobian of a graph, also known as the sandpile group or the critical group, is a finite group abelian group associated to the graph; it has been independently discovered and studied by researchers from various areas. ... -
Topics in percolation and sequence analysis
(Georgia Institute of Technology, 2018-07-02)This thesis studies three topics, two in percolation system and one in sequence analysis. In the first part, we prove that, for directed Bernoulli last passage percolation with i.i.d.~weights on vertices over a $n\times ... -
Local space and time scaling exponents for diffusion on compact metric spaces
(Georgia Institute of Technology, 2018-06-08)We provide a new definition of a local walk dimension beta that depends only on the metric and not on the existence of a particular regular Dirichlet form or heat kernel asymptotics. Moreover, we study the local Hausdorff ... -
Modeling, predicting, and guiding users' temporal behaviors
(Georgia Institute of Technology, 2018-05-11)The increasing availability and granularity of temporal event data produced from user activities in online media, social networks and health informatics provide new opportunities and challenges to model and understand user ... -
Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model
(Georgia Institute of Technology, 2018-04-06)We prove that the evolution of the "most chaotic" dynamical systems consists of three different stages. Consider a finite Markov partition (coarse graining) X of the phase space of a system. In the first short time interval ... -
Nonnegative matrix factorization for text, graph, and hybrid data analytics
(Georgia Institute of Technology, 2018-04-10)Constrained low rank approximation is a general framework for data analysis, which usually has the advantage of being simple, fast, scalable and domain general. One of the most known constrained low rank approximation ... -
Characterization of matrix valued BMO by commutators and sparse domination of operators
(Georgia Institute of Technology, 2018-03-29)In the first part of this thesis, we characterize the space of matrix-valued, two-parameters BMO functions by using commutators with the Hilbert transform. The second part deals with domination of certain operators, by ... -
Minors of graphs of large path-width
(Georgia Institute of Technology, 2018-01-22)Let P be a graph with a vertex v such that P-v is a forest and let Q be an outerplanar graph. In 1993 Paul Seymour asked if every two-connected graph of sufficiently large path-width contains P or Q as a minor.mDefine g(H) ... -
Curvature and isoperimetry in graphs
(Georgia Institute of Technology, 2017-10-02)This dissertation concerns isoperimetric and functional inequalities in discrete spaces. The majority of the work concerns discrete notions of curvature. There is also discussion of volume growth in graphs and of expansion ... -
Results on invariant whiskered tori for fibered holomorphic maps and on compensated domains
We present a very general theory that includes results on the persistence of quasi-periodic orbits of systems subject to quasi-periodic perturbations. -
Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing
(Georgia Institute of Technology, 2017-07-26)The first part of this dissertation explores the application of dominating operators in harmonic analysis by sparse operators. We present preliminary results on dominating certain operators by sparse and analogous operators, ... -
Multilinear dyadic operators and their commutators
(Georgia Institute of Technology, 2017-07-24)In this dissertation, we present a systematic study of multilinear dyadic operators and their commutators with locally integrable functions. We obtain a generalized paraproduct decomposition of the pointwise product of two ... -
The boundary method and general auction for optimal mass transportation and Wasserstein distance computation
(Georgia Institute of Technology, 2017-07-11)Numerical optimal transport is an important area of research, but most problems are too large and complex for easy computation. Because continuous transport problems are generally solved by conversion to either discrete ... -
Analysis and numerical methods in solid state physics and chemistry
(Georgia Institute of Technology, 2017-06-08)In the first part of the paper, we consider an atomic model of deposition over a quasi-periodic medium, that is, a quasi-periodic version of the well-known Frenkel-Kontorova model. We consider the problem of whether there ...
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