Browsing Mathematics and Statistics, Department of by Title
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Mathematics Problems and Thinking Mathematically in Undergraduate Mathematics
(20150501)Mathematics is much more than a formal system of procedures and formulae; it is also a way of thinking built on creativity, precision, reasoning, and representation. I present a model for framing the process of doing ... 
Measuring Dependence via Mutual Information
(20111003)Considerable research has been done on measuring dependence between random variables. The correlation coefficient is the most widely studied linear measure of dependence. However, the limitation of linearity limits its ... 
Minimal Presentations of Sofic Shifts and Properties of PeriodicFiniteType Shifts
(20090812)Constrained codes have been used in data storage systems, such as magnetic tapes, CD’s and DVD’s, in order to reduce the likelihood of errors by predictable noise. The study of constrained codes is based on the study of ... 
The Minimum Witt Index of a Graph
(20070917)An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries ... 
Modeling and Analysis of Dynamic Computer Experiments
Dynamic computer experiments which refer to computer experiments with time series outputs have increasingly gained popularity in both science and engineering. Analysis of dynamic computer experiments through statistical ... 
Modelling of Dynamic Computer Experiments with Both Qualitative and Quantitative Variables
Computer experiments are utilized as a popular tool of studying the relationship between responses and the factors that affect them. They are widely used in scientific researches and applications. Dynamic computer experiments ... 
Modelling Pathogen Evolution with Branching Processes
(20100728)Pathogen evolution poses a significant challenge to public health, as efforts to control the spread of infectious diseases struggle to keep up with a shifting target. To better understand this adaptive process, we turn ... 
Moduli Spaces of K3 Surfaces with Large Picard Number
(20110815)Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces ... 
Moduli spaces of vector bundles on toric surfaces
The moduli spaces parametrizing isomorphism classes of vector bundles are poorly understood. For certain choices of the first Chern class and a suitable second Chern class, we show that there exists an ample line bundle ... 
Multitaper HigherOrder Spectral Analysis of Nonlinear Multivariate Random Processes
(20081104)In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper ... 
Multitaper Methods for Cyclostationary Feature Detection in Time Series Data: Application to ACE Interplanetary Magnetic Field Data
In this thesis, a deeper understanding of the theory of cyclostationary processes is sought. Conventional spectrum estimation techniques assume that the data is a realization of a stationary process. If the data is ... 
Multitaper Methods for TimeFrequency Spectrum Estimation and Unaliasing of Harmonic Frequencies
(20090205)This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the WoldCram'er evolutionary spectrum, which is a timedependent ... 
Networked Control Systems with Unbounded Noise under Information Constraints
(20121206)We investigate the stabilization of unstable multidimensional partially observed singlestation, multisensor (singlecontroller) and multicontroller (singlesensor) linear systems controlled over discrete noiseless ... 
A New Approach in Survival Analysis with Longitudinal Covariates
(20100427)In this study we look at the problem of analysing survival data in the presence of longitudinally collected covariates. New methodology for analysing such data has been developed through the use of hidden Markov modeling. ... 
Noncommutative Independences for Pairs of Faces
In noncommutative probability theories, many different notions of independence arise in various contexts. According to the early classification work, there are only five such notions that are universal/natural in the sense ... 
Nonholonomic mechanics and locomotion: the snakeboard example
(IEEE, 1994)Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard.1 Although the model exhibits basic gait patterns seen in a large number of ... 
Nonparametric and Parametric Methods for Solar Oscillation Spectra
(20140927)The study of the systematic oscillations of the Sun has led to better understanding of the Sun’s inner structure and dynamics, and may help to resolve inconsistencies between observations and the standard solar model. ... 
Nonparametric statistical procedures for therapeutic clinical trials with survival endpoints
(20070802)This thesis proposed two nonparametric statistical tests, based on the KolmogorovSmirnov distance and L2 mallows disatnce. To implement the proposed tests, nonparametric bootstrap method is employed to approximate the ... 
Nonparametric Testing Methods for TreatmentBiomarker Interaction based on Local PartialLikelihood
(Wiley, 20150617)In clinical trials, patients with different biomarker features may respond differently to the new treatments or drugs. In personalized medicine, it is important to study the interaction between treatment and biomarkers in ... 
On Malliavin Calculus and Concentration Inequalities
(20140707)We prove new abstract results concerning concentration inequalities and density estimates for Malliavin differentiable random variables. The efficacy of these results are demonstrated by practical computations, such as the ...