Browsing Scholarly Articles by Affiliation of Duke Author(s) "Mathematics"
Now showing items 21-40 of 396
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A mathematical model for histamine synthesis, release, and control in varicosities
(Theoretical Biology and medical Modelling, 2017) -
A Mathematical Theory of Optimal Milestoning (with a Detour via Exact Milestoning)
(2017-04-23)Milestoning is a computational procedure that reduces the dynamics of complex systems to memoryless jumps between intermediates, or milestones, and only retains some information about the probability of these jumps and the ... -
A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula
(Journal of Mathematical Physics, 2009-12-01)Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading ... -
A Merge-Split Proposal for Reversible Monte Carlo Markov Chain Sampling of Redistricting Plans
We describe a Markov chain on redistricting plans that makes relatively global moves. The chain is designed to be usable as the proposal in a Markov Chain Monte Carlo (MCMC) algorithm. Sampling the space of plans amounts ... -
A multiscale butterfly algorithm for multidimensional fourier integral operators
(Multiscale Modeling and Simulation, 2015-01-01)© 2015 Society for Industrial and Applied Mathematics.This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) =∫ <inf>ℝ d</inf>a(x, ξ)e2πiΦ(x,ξ)f(ξ)dξ, ... -
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 stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply ... -
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 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.
