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Modern Geometry-Methods and Applications(Part II. The Geometry and Topology of Manifolds)

Boris Dubrovin, +2 more
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The article was published on 2010-01-01 and is currently open access. It has received 255 citations till now. The article focuses on the topics: Geometry and topology & Computational topology.

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Journal ArticleDOI

A Liouville-operator derived measure-preserving integrator for molecular dynamics simulations in the isothermal?isobaric ensemble

Mark E. Tuckerman, +5 more
- 12 May 2006 - 
TL;DR: In this paper, a measure-preserving reversible geometric integrator for the equations of motion is presented, which preserves the correct phase-space volume element and is demonstrated to perform well in realistic examples.
MonographDOI

Lectures on analytic differential equations

Yu S Il'yashenko, +1 more
TL;DR: Normal forms and desingularization Singular points of planar analytic vector fields Local and global theory of linear systems Functional moduli of analytic classification of resonant germs and their applications Global properties of complex polynomial foliations Appendix as mentioned in this paper.
Journal ArticleDOI

Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I.

Manoussos G. Grillakis, +2 more
- 24 Mar 2010 - 
TL;DR: In this paper, a new nonlinear Schrodinger equation was derived that describes a second-order correction to the usual tensor product approximation for the Hamiltonian evolution of a many-particle system in Bose-Einstein condensation.
Posted Content

The Landscape of Empirical Risk for Non-convex Losses

Song Mei, +2 more
- 22 Jul 2016 - 
TL;DR: In this article, the authors study the landscape of the empirical risk, namely its stationary points and their properties, and establish uniform convergence of the gradient and Hessian of empirical risk to their population counterparts.
Journal ArticleDOI

Scheme to Measure the Topological Number of a Chern Insulator from Quench Dynamics.

Ce Wang, +4 more
- 05 May 2017 - 
TL;DR: It is shown how the topological number of astatic Hamiltonian can be measured from a dynamical quench process, and it is shown that the linking number of the trajectories of the phase vortices determines the phase boundary of the static Hamiltonian.