Browsing Theses and Dissertations by Subject "Mathematics"
Now showing items 120 of 98

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 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 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 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 LOCAL REDUCED BASIS METHOD FOR RISKAVERSE PDE CONSTRAINED OPTIMIZATION AND INVERSE PROBLEMS
(2018)Many physical systems are modeled using partial dierential equations (PDEs) with uncertain or random inputs. For such systems, naively propagating a xed number of samples of the input probability law (or an approximation ... 
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 for the Reeb Graph and Related Concepts
(2014)This thesis is concerned with a structure called the Reeb graph. There are three main problems considered. The first is devising an efficient algorithm for comnstructing the Reeb graph of a simplicial complex with respect ... 
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 ... 
Analyzing Stratified Spaces Using Persistent Versions of Intersection and Local Homology
(20080805)This dissertation places intersection homology and local homology within the framework of persistence, which was originally developed for ordinary homology by Edelsbrunner, Letscher, and Zomorodian. The eventual goal, begun ... 
Applications of Persistent Homology to Time Varying Systems
(2013)This dissertation extends the theory of persistent homology to time varying systems. Most of the previous work has been dedicated to using this powerful tool in topological data analysis to study static point clouds. In ... 
Applications of Spatial Models to Ecology and Social Systems
(2015)Interacting particle systems have been applied to model the spread of infectious diseases and opinions, interactions between competing species, and evolution of forest landscapes. In this thesis, we study three spatial models ... 
Applications of Topological Data Analysis and Sliding Window Embeddings for Learning on Novel Features of TimeVarying Dynamical Systems
(2017)This work introduces geometric and topological data analysis (TDA) tools that can be used in conjunction with sliding window transformations, also known as delayembeddings, for discovering structure in time series and dynamical ... 
Approximately Counting Perfect and General Matchings in Bipartite and General Graphs
(2009)We develop algorithms to approximately count perfect matchings in bipartite graphs (or permanents of the corresponding adjacency matrices), perfect matchings in nonbipartite graphs (or hafnians), and general matchings in ... 
Aspects of Motives: Finitedimensionality, ChowKunneth Decompositions and Intersections of Cycles
(2016)This thesis analyzes the Chow motives of 3 types of smooth projective varieties: the desingularized elliptic self fiber product, the Fano surface of lines on a cubic threefold and an ample hypersurface of an Abelian variety. ... 
Aspects of the (0,2)McKay Correspondence
(2015)We study first order deformations of the tangent sheaf of resolutions of CalabiYau threefolds that are of the form $\CC^3/\ZZ_r$, focusing on the cases where the orbifold has an isolated singularity. We prove a lower bound ... 
Asymptotic Behavior of Certain Branching Processes
(2019)This dissertation examines the asymptotic behavior of three branching processes. The first is a branching process with selection; the selection is dictated by a fitness function which is the sum of a linear part and a periodic ... 
Atlas Simulation: A Numerical Scheme for Approximating Multiscale Diffusions Embedded in High Dimensions
(2014)When simulating multiscale stochastic differential equations (SDEs) in highdimensions, separation of timescales and highdimensionality can make simulations expensive. The computational cost is dictated by microscale properties ... 
Augmentations and exact Lagrangian cobordisms
(2017)To a Legendrian knot, one can associate an $A_{\infty}$ category, the augmentation category.An exact Lagrangian cobordism between two Legendrian knots gives a functor of the augmentation categories of the two knots.We study ... 
Augmentations and Rulings of Legendrian Links
(2016)For any Legendrian knot in R^3 with the standard contact structure, we show that the existence of an augmentation to any field of the ChekanovEliashberg differential graded algebra over Z[t,t^{1}] is equivalent to the ...