Discrete vortex representation of magnetohydrodynamics

All-optical discrete vortex switch

Anton S. Desyatnikov,1 Mark R. Dennis,2 and Albert Ferrando3 1Nonlinear Physics Center, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 0200, Australia 2H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom 3Interdisciplinary Modeling Group, InterTech and Departament d’Optica, Universitat de Valéncia,...

Hamiltonian Representation of Magnetohydrodynamics for Boundary Energy Controls

Discrete vortex solitons and parity time symmetry.

We study the effect of lifting the degeneracy of vortex modes with a parity time (PT) symmetric defect, using discrete vortices in a circular array of nonlinear waveguides as an example. When the defect is introduced, the degenerate linear vortex modes spontaneously break PT symmetry and acquire complex eigenvalues, but nonlinear propagating modes with real propagation constants can still exist...

Neural Discrete Representation Learning

Learning useful representations without supervision remains a key challenge in machine learning. In this paper, we propose a simple yet powerful generative model that learns such discrete representations. Our model, the Vector QuantisedVariational AutoEncoder (VQ-VAE), differs from VAEs in two key ways: the encoder network outputs discrete, rather than continuous, codes; and the prior is learnt...

Implicit Representation of Discrete Objects

This tutorial paper discusses the known representations based on Binary Decision Diagrams (BDDs) for various types of discrete objects: incompletely specified functions, sets, finite state machines, binary and multi-valued relations, etc. While presenting the known material, the emphasis is on those aspects of implicit representations that are important to achieve speed-up in computation. The n...