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

The back and forth error compensation and correction method for linear hyperbolic systems and a conservative BFECC limiter
(Georgia Institute of Technology, 20180725)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, 20180723)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, 20180731)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, 20180702)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, 20180608)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, 20180511)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 windtree model
(Georgia Institute of Technology, 20180406)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, 20180410)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, 20180329)In the first part of this thesis, we characterize the space of matrixvalued, twoparameters BMO functions by using commutators with the Hilbert transform. The second part deals with domination of certain operators, by ... 
Minors of graphs of large pathwidth
(Georgia Institute of Technology, 20180122)Let P be a graph with a vertex v such that Pv is a forest and let Q be an outerplanar graph. In 1993 Paul Seymour asked if every twoconnected graph of sufficiently large pathwidth contains P or Q as a minor.mDefine g(H) ... 
Curvature and isoperimetry in graphs
(Georgia Institute of Technology, 20171002)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 quasiperiodic orbits of systems subject to quasiperiodic perturbations. 
Weighted inequalities via dyadic operators and a learning theory approach to compressive sensing
(Georgia Institute of Technology, 20170726)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, 20170724)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, 20170711)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, 20170608)In the first part of the paper, we consider an atomic model of deposition over a quasiperiodic medium, that is, a quasiperiodic version of the wellknown FrenkelKontorova model. We consider the problem of whether there ... 
Mathematical problems concerning the Kac model
(Georgia Institute of Technology, 20170523)This thesis deals with the Kac model in kinetic theory. Kac’s model is a linear, space homogeneous, nparticle model created by Mark Kac in 1956 in [14] in an attempt to give a derivation of Boltzmann’s equation. The ... 
Inflation of a planar domain
(Georgia Institute of Technology, 20170504)Take a soap film or other capillary surface that spans a fixed boundary at one end of a container and bounds the volume inside. If you increase the pressure in the bounded volume the soap film will expand outwards into the ... 
Subdivisions of complete graphs
(Georgia Institute of Technology, 20170523)A subdivision of a graph G, also known as a topological G and denoted by TG, is a graph obtained from G by replacing certain edges of G with internally vertexdisjoint paths. This dissertation studies a problem in structural ... 
Statistical inference for some risk measures
(Georgia Institute of Technology, 20170503)Recently, many risk measures have been developed for various types of risk based on multiple financial variables. However, statistical properties of these risk measures are not fully understood, and there are very few ...