Browsing Scholarly Articles by Affiliation of Duke Author(s) "Mathematics"
Now showing items 2140 of 355

A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices
(The Annals of Applied Probability, 201806) 
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 phylogenetic transform enhances analysis of compositional microbiota data.
(Elife, 20170215)Surveys of microbial communities (microbiota), typically measured as relative abundance of species, have illustrated the importance of these communities in human health and disease. Yet, statistical artifacts commonly plague ... 
A population model of folatemediated onecarbon metabolism.
(Nutrients, 20130705)BACKGROUND: Previous mathematical models for hepatic and tissue onecarbon metabolism have been combined and extended to include a blood plasma compartment. We use this model to study how the concentrations of metabolites ... 
A practical criterion for positivity of transition densities
(Nonlinearity, 20150710)© 2015 IOP Publishing Ltd & London Mathematical Society.We establish a simple criterion for locating points where the transition density of a degenerate diffusion is strictly positive. Throughout, we assume that the diffusion ... 
A quantum analogue of the dihedral action on Grassmannians
(Journal of Algebra, 201206) 
A Quantum Kinetic Monte Carlo Method for Quantum Manybody Spin Dynamics
(20171130)We propose a general framework of quantum kinetic Monte Carlo algorithm, based on a stochastic representation of a series expansion of the quantum evolution. Two approaches have been developed in the context of quantum manybody ... 
A quasinonlocal coupling method for nonlocal and local diffusion models
(20170423)In this paper, we extend the idea of "geometric reconstruction" to couple a nonlocal diffusion model directly with the classical local diffusion in one dimensional space. This new coupling framework removes interfacial ... 
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 solution of a problem of Sophus Lie: Normal forms of twodimensional metrics admitting two projective vector fields
(Mathematische Annalen, 20080201)We give a complete list of normal forms for the twodimensional metrics that admit a transitive Lie pseudogroup of geodesicpreserving transformations and we show that these normal forms are mutually nonisometric. This ... 
A Surface Hopping Gaussian Beam Method for HighDimensional Transport Systems
(20170423)We propose a surface hopping Gaussian beam method to numerically solve a class of high frequency linear transport systems in high spatial dimensions, based on asymptotic analysis. The stochastic surface hopping is combined ... 
A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs
(Electronic Journal of Probability, 20110509)We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. ... 
A topological introduction to knot contact homology
(Bolyai Society Mathematical Studies, 20140101)This is a survey of knot contact homology, with an emphasis on topological, algebraic, and combinatorial aspects. 
A universal magnification theorem. II. Generic caustics up to codimension five
(Journal of Mathematical Physics, 20090909)We prove a theorem about magnification relations for all generic general caustic singularities up to codimension five: folds, cusps, swallowtail, elliptic umbilic, hyperbolic umbilic, butterfly, parabolic umbilic, wigwam, ... 
A Variation on the DonskerVaradhan Inequality for the Principial Eigenvalue
(20170423)The purpose of this short note is to give a variation on the classical DonskerVaradhan inequality, which bounds the first eigenvalue of a secondorder elliptic operator on a bounded domain $\Omega$ by the largest mean first ... 
A variational perspective on cloaking by anomalous localized resonance
(Communications in Mathematical Physics, 20140314)© SpringerVerlag Berlin Heidelberg 2014.A body of literature has developed concerning “cloaking by anomalous localized resonance.” The mathematical heart of the matter involves the behavior of a divergenceform elliptic ... 
A weak trapezoidal method for a class of stochastic differential equations
(Communications in Mathematical Sciences, 20110301)We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations ... 
Accelerated sampling by infinite swapping of path integral molecular dynamics with surface hopping
(20171130)To accelerate the thermal equilibrium sampling of multilevel quantum systems, the infinite swapping limit of a recently proposed multilevel ring polymer representation is investigated. In the infinite swapping limiting, ... 
Adaptive local basis set for KohnSham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
(Journal of Computational Physics, 20120220)KohnSham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the KohnSham Hamiltonian generally results in a large number ... 
Adaptive temporal compressive sensing for video
(2013 IEEE International Conference on Image Processing, ICIP 2013  Proceedings, 20131201)This paper introduces the concept of adaptive temporal compressive sensing (CS) for video. We propose a CS algorithm to adapt the compression ratio based on the scene's temporal complexity, computed from the compressed data, ...