Mathematics, Statistics, and Computer Science, Department of
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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 ... 
Rigid MultiMotion Optical Flow Estimation
(20180112)Optical flow is a fundamental problem in computer vision. Given a pair of image frames from a video source, the objective is to estimate the movement, or translation of pixels in the second image with respect to the first ... 
An Iterative Spectral Approach to Recovering Planted Partitions
(20180406)In the planted partition problem, the n vertices of a random graph are partitioned into k "clusters," and edges between vertices in the same cluster and different clusters are included with constant probability p and q, ... 
Towards High Performance Determinism for Multithreaded Programs
(20180419)The emergence of multicore commodity processors, and more recently accelerators, has brought about a resurgence of interest in parallel programming. With that renewed interest comes a concern amongst practitioners and ... 
Algorithms and Implementations in Computational Algebraic Geometry
(20180327)In this thesis, we explore several areas of computational algebraic geometry, and develop new algorithms and software in each. We are generally interested in solving polynomial systems and applications that require solving ... 
New Models and Algorithms for Data Analysis
(20180411)In this thesis, we introduce and analyze new models and new algorithms for problems in data analysis. Many new challenges and constraints for data analysis have arisen as data analysis has become increasingly important. ... 
Computing Series Expansions of Algebraic Space Curves
(20180402)We work towards a seriesbased computational approach for polynomial systems having positivedimensional solution sets. The tropical variety gives information on the exponents of the leading terms of the series; we provide ... 
Improving Web Privacy And Security with a CostBenefit Analysis of the Web API
(20180417)Over the last two decades, the web has grown from a system for delivering static documents, to the world’s most popular application platform. As the web has become more popular and successful, browser vendors have added ... 
Supporting Navigation with a Torso Wearable Tactile Display
(20180410)An estimated 253 million people in the world are blind and visually impaired. Visual impairments can significantly lower one's quality of life as they hamper the ability to perform otherwise simple tasks, like cooking a ... 
Visual Analysis Techniques for Dynamic Biological Networks
(20180409)Due to the complexity of biological data that can be collected, modeled and analyzed thanks to technological and algorithmic advancements, the difficulty in studying biological networks has increased over the last decades. ... 
Optimal Design for Nonlinear Model with Random Eﬀect and InformationBased Subdata Selection for LASSO
(20171220)Optimal designs for nonlinear model with random block eﬀects are systematically studied. For a large class of nonlinear models, we prove that any optimal design can be based on some simple structures. We further derive the ... 
DecisionTheoretic Monitoring of CyberPhysical Systems
(20180413)Cyberphysical systems (CPS) represent "engineered systems that are built from, and depend upon, the seamless integration of computational algorithms and physical components". They can be found in such areas as aerospace, ... 
Hellinger Information and Optimal Design for Nonregular Models
(20180316)Classically, the Fisher information is the relevant object for defining optimal experimental designs. However, for models that lack certain regularity, the Fisher information does not exist and, hence, no notion of design ... 
Arithmetic Properties of the Frobenius Traces Defined by a Rational Abelian Variety (with two appendices by JP. Serre)
(Oxford University Press, 201706)Let A be an abelian variety over Q of dimension g such that the image of its associated absolute Galois representation rho(A) is open in GSp(2g)((Z) over cap). We investigate the arithmetic of the traces a(1,p) of the ... 
Nuclear norm of higherorder tensors
(American Mathematical Society, 201611)We establish several mathematical and computational properties of the nuclear norm for higherorder tensors. We show that like tensor rank, tensor nuclear norm is dependent on the choice of base field  the value of the ... 
NUMERICAL SIMULATION OF GRATING STRUCTURES INCORPORATING TWODIMENSIONAL MATERIALS: A HIGHORDER PERTURBATION OF SURFACES FRAMEWORK
(Society for Industrial and Applied Mathematics, 20180102)The plasmonics of twodimensional materials, such as graphene, has become an important field of study for devices operating in the terahertz to midinfrared regime where such phenomena are supported. The semimetallic character ... 
AVERAGING OF NONLINEAR SCHRODINGER EQUATIONS ¨ WITH STRONG MAGNETIC CONFINEMENT
(International Press, 201611)We consider the dynamics of nonlinear Schrödinger equations with strong constant magnetic fields. In an asymptotic scaling limit the system exhibits a purely magnetic confinement, based on the spectral properties of the ... 
Nonparametric Independence Screening via Favored Smoothing Bandwidth
(Elsevier, 20171123)We propose a flexible nonparametric regression method for ultrahighdimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. ... 
Functional envelope for modelfree sufficient dimension reduction
(Elsevier, 201710)In this article, we introduce the functional envelope for sufficient dimension reduction and regression with functional and longitudinal data. Functional sufficient dimension reduction methods, especially the inverse ... 
The tensor rank of tensor product of two threequbit W states is eight
(Elsevier, 201708)We show that the tensor rank of tensor product of two threequbit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor ...