Browsing Scholarly Articles by Affiliation of Duke Author(s) "Mathematics"
Now showing items 2140 of 396

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)
(20170423)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 KacRice formula
(Journal of Mathematical Physics, 20091201)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 MergeSplit 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, 20150101)© 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, 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 stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBMSVGD, 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 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 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.