Browsing Duke Scholarly Works by Affiliation of Duke Author(s) "Mathematics"
Now showing items 120 of 338

(1,1) Lspace knots
(COMPOSITIO MATHEMATICA, 20180501)We characterize the (1, 1) knots in the threesphere and lens spaces that admit nontrivial Lspace surgeries. As a corollary, 1bridge braids in these manifolds admit non trivial Lspace surgeries. We also recover ... 
A combinatorial spanning tree model for knot Floer homology
(Advances in Mathematics, 201210) 
A complete knot invariant from contact homology
We construct an enhanced version of knot contact homology, and show that we can deduce from it the group ring of the knot group together with the peripheral subgroup. In particular, it completely determines a knot up to ... 
A consistent hierarchy of generalized kinetic equation approximations to the master equation applied to surface catalysis.
(J Chem Phys, 20150621)We develop a hierarchy of approximations to the master equation for systems that exhibit translational invariance and finiterange spatial correlation. Each approximation within the hierarchy is a set of ordinary differential ... 
A convergent method for linear halfspace kinetic equations
(20170423)We give a unified proof for the wellposedness of a class of linear halfspace equations with general incoming data and construct a Galerkin method to numerically resolve this type of equations in a systematic way. Our main ... 
A De RhamWitt approach to crystalline rational homotopy theory
(COMPOSITIO MATHEMATICA, 200409) 
A DeepLearning Algorithm for Thyroid Malignancy Prediction From Whole Slide Cytopathology Images
We consider thyroidmalignancy prediction from ultrahighresolution wholeslide cytopathology images. We propose a deeplearningbased algorithm that is inspired by the way a cytopathologist diagnoses the slides. The algorithm ... 
A Diabatic Surface Hopping Algorithm based on Time Dependent Perturbation Theory and Semiclassical Analysis
(20171130)Surface hopping algorithms are popular tools to study dynamics of the quantumclassical mixed systems. In this paper, we propose a surface hopping algorithm in diabatic representations, based on time dependent perturbation ... 
A dimensionless number for understanding the evolutionary dynamics of antigenically variable RNA viruses.
(Proc Biol Sci, 20111222)Antigenically variable RNA viruses are significant contributors to the burden of infectious disease worldwide. One reason for their ubiquity is their ability to escape herd immunity through rapid antigenic evolution and ... 
A fast algorithm for multilinear operators
(Applied and Computational Harmonic Analysis, 2012)This paper introduces a fast algorithm for computing multilinear integrals which are defined through Fourier multipliers. The algorithm is based on generating a hierarchical decomposition of the summation domain into squares, ... 
A geodesicbased Riemannian gradient approach to averaging on the Lorentz group
(Entropy, 20171228) 
A Hybrid Globallocal Numerical Method for Multiscale PDEs
(20170423)We present a new hybrid numerical method for multiscale partial differential equations, which simultaneously captures both the global macroscopic information and resolves the local microscopic events. The convergence of ... 
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 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 ...