Browsing by Subject "Mathematics"
Now showing items 1-20 of 185
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(1,1) L-space knots
(COMPOSITIO MATHEMATICA, 2018-05-01)We characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space 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, 2020-06-15)© 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 Deep Learning Model for V50%, V60%, and V66.7% Prediction in LINAC-based Treatment Planning of Single-Iso-Multiple-Targets (SIMT) Stereotactic Radiosurgery (SRS)
(2023)Brain metastases are a common complication of many types of cancer, including lung, breast, and melanoma. Approximately 30-40% of patients develop brain metastases that originate from primary systemic tumors during the course ... -
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)Noise-induced 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), 2015-01)Three-dimensional 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 ZEROTH-ORDER ORACLE FOR DISTRIBUTED AND NON-STATIONARY LEARNING
(2021)Zeroth-Order (ZO) methods have been applied to solve black-box or simulation-based 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, 2016-08-29)© 2016 American Mathematical Society. From Furuta’s 10/8 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4-manifold whose boundary is 0-surgery 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 stochastic-Lagrangian particle system for the Navier-Stokes equations
(Nonlinearity, 2008-11-01)This paper is based on a formulation of the Navier-Stokes 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
(2012-04-26)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
(2007-07-31)We here developed a third-order 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 Phase-Field 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, quasi-brittle fracture, cohesive fracture, and ductile fracture. Predicting fracture ... -
Absolute Continuity of Singular SPDEs and Bayesian Inference on Dynamical Systems
(2023)We explore the interplay among probability, stochastic analysis, and dynamical systems through two lenses: (1) absolute continuity of singular stochastic partial differential equations (SPDEs); (2) Bayesian inference on ... -
ADAPTIVE LOCAL REDUCED BASIS METHOD FOR RISK-AVERSE 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 ... -
Advances in Choquet theories
(2022)Choquet theory and the theory of capacities, both initiated by French mathematician Gustave Choquet, share the heuristic notion of studying the extrema of a convex set in order to give interesting results regarding its elements. ... -
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 adaptive Euler-Maruyama scheme for SDEs: Convergence and stability
(IMA Journal of Numerical Analysis, 2007-01-01)The understanding of adaptive algorithms for stochastic differential equations (SDEs) is an open area, where many issues related to both convergence and stability (long-time behaviour) of algorithms are unresolved. This ... -
An Empirical Comparison of Multiple Imputation Methods for Categorical Data
(The American Statistician, 2017-04-03)© 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 ...
