Browsing by Department "Mathematics"
Now showing items 120 of 151

A Bargaining Theory of the “Edwards’ Effect” in the 20078 Democratic Presidential Primary
(2009)2008’s Democratic Presidential Primary will go down as one of the most competitive races in recent history. Two candidates, Senators Barack Obama (Illinois) and Hillary Clinton (New York), fought a seesaw battle to obtain ... 
A Closer Look at ADC Multivariate GARCH
(20090504)In the past thirty years, academia and the marketplace have devoted signi cant e ort and resources toward gaining a better understanding of how volatility changes over time in the nancial markets and how changes in one ... 
A Dynamical Nephrovascular Model of Renal Autoregulation
(2014)The main functions of the kidney take place in the nephrons. For their proper operation, nephrons need to be supplied with a stable blood flow that remains constant despite fluctuations of arterial pressure. Such stability ... 
A Generalized Lyapunov Construction for Proving Stabilization by Noise
(2012)Noiseinduced stabilization occurs when an unstable deterministic system is stabilized by the addition of white noise. Proving that this phenomenon occurs for a particular system is often manifested through the construction ... 
A maximum entropybased approach for the description of the conformational ensemble of calmodulin from paramagnetic NMR
(20160504)Characterizing protein dynamics is an essential step towards a better understanding of protein function. Experimentally, we can access information about protein dynamics from paramagnetic NMR data such as pseudocontact shifts, ... 
A Model of Speculative Attacks and Devaluations in Korea and Indonesia
(2009)Since the beginning of the Bretton Woods era, currency crises and speculative attacks have affected the world economy. This paper presents a model, originally derived by Blanco and Garber, that predicts oneperiod ahead ... 
A Model of the Foot and Ankle in Running
(20110511)We present several variations on a model and simulation of the foot and ankle during the course of one running stride. We summarize the motivation behind the model and similar work in the field, then describe the model and ... 
A Simple Cardiac Model Exhibiting Stationary Discordant Alternans
(20110425)The term alternans refers to a perioddoubling bifurcation that occurs in rapidlypaced cardiac cells: although all stimuli are equally spaced, short and long action potentials alternate with one another. Cardiac waves ... 
A Spectral Deferred Correction Method for Solving Cardiac Models
(2011)Many numerical approaches exist to solving models of electrical activity in the heart. These models consist of a system of stiff nonlinear ordinary differential equations for the voltage and other variables governing channels, ... 
A Stochastic Spatial Model for Tumor Growth
(20140429)Evolutionary game theory can be used to study the interactions of different cell phenotypes and describe tumor population dynamics. Instead of killing tumor cells, clinical treatment could aim to change the nature of the ... 
A Strategy and Honesty Based Comparison of Preferential Ballot Voting Methods
(20130502)This paper presents an analysis of various preferential ballot voting systems based on the idea that voters should be encouraged to vote honestly and independently of the other votes cast. Random votes are simulated in three ... 
A Study of Edge Toric Ideals using Associated Graphs
(20120426)This thesis studies properties of edge toric ideals and resolutions by analyzing the associated graphs of algebraic structures. It mainly focused on proving that the repeated edges in a graph wouldn't change some properties ... 
A Theory of Optimal Sick Pay
(2009)Illness significantly reduces worker productivity, yet how employers respond to the possibility of illness and its effects on work performance is not well understood. The 2003 American Productivity Audit pegged the cost ... 
A Third Order Numerical Method for Doubly Periodic Electromegnetic Scattering
(20070731)We here developed a thirdorder accurate numerical method for scattering of 3D electromagnetic waves by doubly periodic structures. The method is an intuitively simple numerical scheme based on a boundary integral formulation. ... 
Adaptive Data Representation and Analysis
(2018)This dissertation introduces and analyzes algorithms that aim to adaptively handle complex datasets arising in the realworld applications. It contains two major parts. The first part describes an adaptive model of 1dimensional ... 
Algebraic De Rham Theory for Completions of Fundamental Groups of Moduli Spaces of Elliptic Curves
(2018)To study periods of fundamental groups of algebraic varieties, one requires an explicit algebraic de Rham theory for completions of fundamental groups. This thesis develops such a theory in two cases. In the first case, ... 
Algorithms with Applications to Anthropology
(2018)In this dissertation, we investigate several problems in shape analysis. We start by discussing the shape matching problem. Given that homeomorphisms of shapes are computed in practice by interpolating sparse correspondence, ... 
An Application of Abstract Algebra to the Neural Code for Sound Localization in the Barn Owl
(20160425)Patterns of neural firing can be viewed as a binary code with each neuron as a bit, with neurons which actively fire in response to a stimulus associated to a 1 and those which do not fire associated to a 0. In previous ... 
An Investigation into the Interdependency of the Volatility of Technology Stocks
(200904)This paper examines the contemporaneous and dynamic relationships between the volatilities of the technology stocks in the S&P 100 index. Factor analysis and heterogeneous autoregressive regressions are used to ... 
Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics
(2016)The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian ...