Browsing Scholarly Articles by Affiliation of Duke Author(s) "Mathematics"
Now showing items 21-40 of 355
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A necessary and sufficient condition for edge universality at the largest singular values of covariance matrices
(The Annals of Applied Probability, 2018-06) -
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 phylogenetic transform enhances analysis of compositional microbiota data.
(Elife, 2017-02-15)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 folate-mediated one-carbon metabolism.
(Nutrients, 2013-07-05)BACKGROUND: Previous mathematical models for hepatic and tissue one-carbon 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, 2015-07-10)© 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, 2012-06) -
A Quantum Kinetic Monte Carlo Method for Quantum Many-body Spin Dynamics
(2017-11-30)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 many-body ... -
A quasinonlocal coupling method for nonlocal and local diffusion models
(2017-04-23)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, 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 solution of a problem of Sophus Lie: Normal forms of two-dimensional metrics admitting two projective vector fields
(Mathematische Annalen, 2008-02-01)We give a complete list of normal forms for the two-dimensional metrics that admit a transitive Lie pseudogroup of geodesic-preserving transformations and we show that these normal forms are mutually non-isometric. This ... -
A Surface Hopping Gaussian Beam Method for High-Dimensional Transport Systems
(2017-04-23)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, 2011-05-09)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, 2014-01-01)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, 2009-09-09)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 Donsker-Varadhan Inequality for the Principial Eigenvalue
(2017-04-23)The purpose of this short note is to give a variation on the classical Donsker-Varadhan inequality, which bounds the first eigenvalue of a second-order 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, 2014-03-14)© Springer-Verlag 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 divergence-form elliptic ... -
A weak trapezoidal method for a class of stochastic differential equations
(Communications in Mathematical Sciences, 2011-03-01)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
(2017-11-30)To accelerate the thermal equilibrium sampling of multi-level quantum systems, the infinite swapping limit of a recently proposed multi-level ring polymer representation is investigated. In the infinite swapping limiting, ... -
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
(Journal of Computational Physics, 2012-02-20)Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamiltonian generally results in a large number ... -
Adaptive temporal compressive sensing for video
(2013 IEEE International Conference on Image Processing, ICIP 2013 - Proceedings, 2013-12-01)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, ...
