Mathematics, Statistics, and Computer Science, Department of
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Extremal Problems on Directed Hypergraphs and the ErdösGyárfás Ramsey Problem Variant for Graphs
(20180530)Let a 2 to 1 directed hypergraph be a 3uniform hypergraph where every edge has two tail vertices and one head vertex. For any such directed hypergraph F let the nth extremal number of F be the maximum number of edges that ... 
Topological Equivalences of Einfinity Differential Graded Algebras
(20180618)Two DGAs are said to be topologically equivalent when the corresponding Eilenberg–Mac Lane ring spectra are weakly equivalent as ring spectra. Quasiisomorphic DGAs are topologically equivalent, but the converse is not ... 
ScoreMatching Representative Approach for Big Data Analysis with Generalized Linear Models
(20180710)We propose a fast and efficient strategy, called the representative approach, with linear models and generalized linear models for big data analysis, and in particular for distributed dataset. With a given partitioning of ... 
Shape Theory in Homotopy Theory and Algebraic Geometry
(20180615)This work defines the étale homotopy type in the context of nonarchimedean geometry, in both Berkovich’s and Huber’s formalisms. To do this we take the shape of a site’s associated hypercomplete 1topos. This naturally ... 
Effects of Audio Dilation and Listening Skill Ability for English as a Second Language
(20180615)This project examines the effects of an audio dilation technique to slow the speech rate of audio for English as a Second language individuals, using listening skill assessment tests from the Test of English as a Foreign ... 
Ensuring Privacy in Legacy Web Applications through Multiple Relations Views
(20180606)This thesis is focused on the protection of legacy Web Applications against information leakage as well as the defense against well known attacks such as some form of SQLInjection. Many legacy Web Applications are unsafe ... 
Effective Divisors on Kontsevich Moduli Spaces
(20180511)We study the cone of effective divisors on Kontsevich's moduli space of genus 0 stable maps to projective space in the case where map is equipped with a marked point on the domain curve, extending previous work of Coskun, ... 
Broad Learning in Multiple Heterogeneous Domains
(20180417)Recent years have witnessed the flourishing of heterogeneous data from various types of domains. For example, online review sites (like Amazon and Yelp) have access to contextual information of shopping histories of users, ... 
Scales, Diamond and the Strong Tree Property
(20180820)In this thesis, I prove two consistency results in set theory. The first concerns GCH, very good and bad scales, and the failure of diamond at the successor of a singular. The second concerns the failure of SCH and arbitrary ... 
A Nonlinear Least Squares Framework for Periodic Grating Identification with a HOPS Implementation
(20180801)This thesis focuses upon the scattering of timeharmonic plane waves by a periodic interface. In particular, we consider an inverse problem which involves reconstruction of the interface when provided with measured scattered ... 
Reliability Issues among Android Components: Analysis, Testing and Solutions
(20180801)Reliability is one of the aspects at the core of every operating system for its impact on the user experience. We explore the current status of the reliability in the interactions among Android applications components, ... 
Hausdorff Dimension of Kuperberg Minimal Sets
(20180727)In 1994, Kuperberg constructed a smooth flow on a threemanifold with no periodic orbits. It was later shown that a generic Kuperberg flow preserves a codimension one laminar minimal set. We develop new techniques to study ... 
ETNA: a Virtual Reality Game with Affective Dynamic Difficulty Adjustment based on Skin Conductance
(20180718)The video game industry is growing year after year, but one of the main problems that most developers have is how to address the right difficulty of a game to satisfy all the players that have different skills and different ... 
Robust Prediction Methods for Covariate Shift and Active Learning
(20180802)In real world machine learning applications, it is often not very realistic to assume that the training data distribution aligns with the testing data distribution. A relaxation is to assume the distribution shift only ... 
Regularity and Energy Laws in Hydrodynamic Models of Newtonian Fluids and Collective Behavior
(20180612)We consider several hydrodynamic models of Newtonian fluids and collective behavior, including the Euler and NavierStokes equations (both homogeneous and inhomogeneous) as well as the fractional Euler Alignment model. ... 
A review on probabilistic models used in microbiome studies
(International Press, 20180201) 
Well–Posedness and Analyticity of Solutions to a Water Wave Problem with Viscosity
(Elsevier, 20180430)The water wave problem models the free–surface evolution of an ideal fluid under the influence of gravity and surface tension. The governing equations are a central model in the study of open ocean wave propagation, but ... 
TRANSVERSE NONCOMMUTATIVE GEOMETRY OF FOLIATIONS
(Elsevier, 20180907)We define an L2signature for proper actions on spaces of leaves of transversely oriented foliations with bounded geometry. This is achieved by using the Connes fibration to reduce the problem to the case of Riemannian ... 
An efficient timesplitting method for the ehrenfest dynamics
(Society for Industrial and Applied Mathematics, 20170806)The Ehrenfest dynamics, representing a quantumclassical meanfield type coupling, is a widely used approximation in quantum molecular dynamics. In this paper, we propose a timesplitting method for an Ehrenfest dynamics, ... 
Broad Learning for Healthcare
(20180327)A broad spectrum of data from different modalities are generated in the healthcare domain every day, including scalar data (e.g., clinical measures collected at hospitals), tensor data (e.g., neuroimages analyzed by research ...