Browsing by Subject "Mathematics"
Now showing items 120 of 154

(1,1) Lspace knots
(COMPOSITIO MATHEMATICA, 20180501)We characterize the (1, 1) knots in the threesphere and lens spaces that admit nontrivial Lspace surgeries. As a corollary, 1bridge braids in these manifolds admit non trivial Lspace surgeries. We also recover ... 
A classical proof that the algebraic homotopy class of a rational function is the residue pairing
(Linear Algebra and Its Applications, 20200615)© 2020 Elsevier Inc. Cazanave has identified the algebraic homotopy class of a rational function of 1 variable with an explicit nondegenerate symmetric bilinear form. Here we show that Hurwitz's proof of a classical result ... 
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 new fully automated approach for aligning and comparing shapes.
(Anatomical record (Hoboken, N.J. : 2007), 201501)Threedimensional geometric morphometric (3DGM) methods for placing landmarks on digitized bones have become increasingly sophisticated in the last 20 years, including greater degrees of automation. One aspect shared by ... 
A NEW ZEROTHORDER ORACLE FOR DISTRIBUTED AND NONSTATIONARY LEARNING
(2021)ZerothOrder (ZO) methods have been applied to solve blackbox or simulationbased optimization prroblems. These problems arise in many important applications nowa days, e.g., generating adversarial attacks on machine learning ... 
A slicing obstruction from the $\frac {10}{8}$ theorem
(Proceedings of the American Mathematical Society, 20160829)© 2016 American Mathematical Society. From Furuta’s 10/8 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4manifold whose boundary is 0surgery on a knot. We show that this obstruction is able ... 
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 stochasticLagrangian particle system for the NavierStokes equations
(Nonlinearity, 20081101)This paper is based on a formulation of the NavierStokes equations developed by Constantin and the first author (Commun. Pure Appl. Math. at press, arXiv:math.PR/0511067), where the velocity field of a viscous incompressible ... 
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. ... 
A Variational Framework for PhaseField Fracture Modeling with Applications to Fragmentation, Desiccation, Ductile Failure, and Spallation
(2021)Fracture is a common phenomenon in engineering applications. Many types of fracture exist, including, but not limited to, brittle fracture, quasibrittle fracture, cohesive fracture, and ductile fracture. Predicting fracture ... 
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 ... 
An Empirical Comparison of Multiple Imputation Methods for Categorical Data
(The American Statistician, 20170403)© 2017 American Statistical Association. Multiple imputation is a common approach for dealing with missing values in statistical databases. The imputer fills in missing values with draws from predictive models estimated ... 
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 ...