• Topics on the Longest Common Subsequences: Simulations, Computations, and Variance 

  Liu, Qingqing (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 

  Zhou, Fan (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 

  Hebbe Madhusudhana, Bharath (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 

  Scott, Shane (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 ...

• Locally decodable codes and arithmetic progressions in random settings 

  Gopi, Sivakanth (2018-11-09)

  (1) A set D of natural numbers is called t-intersective if every positive upper density subset A of natural numbers contains a (t+1)-length arithmetic progression (AP) whose common differences is in D. Szemeredi's theorem ...

• Large girth approximate Steiner triple systems 

  Warnke, Lutz (2018-09-28)

  In 1973 Erdos asked whether there are n-vertex partial Steiner triple systems with arbitrary high girth and quadratically many triples. (Here girth is defined as the smallest integer g \ge 4 for which some g-element ...

• The back and forth error compensation and correction method for linear hyperbolic systems and a conservative BFECC limiter 

  Wang, Xin (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 

  Chen, Tongzhou (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​ 

  Yuen, Chi Ho (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 

  Xu, Chen (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 

  Dever, John William (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 

  Wang, Yichen (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 ...

• Multiscale and stochastic methods for inverse source problems and signal analysis 

  Zhou, Haomin (Georgia Institute of Technology, 2014-09-30)

• Topics in dynamics: First passage probabilities and chaotic properties of the physical wind-tree model 

  Bolding, Mark M. (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 

  Du, Rundong (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 

  Mena Arias, Dario Alberto (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 

  Dang, Thanh Ngoc (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) ...

• Multi-frequency oscillations in biological, electrical, and mechanical systems 

  Yi, Yingfei (Georgia Institute of Technology, 2010-06-05)

• FRG: Collaborative research: Applications of transportation theory to nonlinear dynamics 

  Gangbo, Wilfrid; Evans, Lawrence; Caffarelli, Luis; McCann, Robert; Feldman, Mikhail; Cullen, Mike (Georgia Institute of Technology, 2009-08-05)

• Classical problems in differential geometry, topology, and convexity 

  Ghomi, Mohammad; Stojanovic, Gordana (Georgia Institute of Technology, 2009-07-03)

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