241,157 research outputs found
The Gauge-Bethe Correspondence and Geometric Representation Theory
The Gauge/Bethe correspondence of Nekrasov and Shatashvili relates the
spectrum of integrable spin chains to the ground states of supersymmetric gauge
theories. Up to now, this correspondence has been an observation; the
underlying reason for its existence remaining elusive. We argue here that
geometrical representation theory is the mathematical foundation of the
Gauge/Bethe correspondence, and it provides a framework to study families of
gauge theories in a unified way.Comment: 8 page
Corrections to "Unified Laguerre polynomial-series-based distribution of small-scale fading envelopes''
In this correspondence, we point out two typographical errors in Chai and
Tjhung's paper and we offer the correct formula of the unified Laguerre
polynomial-series-based cumulative distribution function (cdf) for small-scale
fading distributions. A Laguerre polynomial-series-based cdf formula for
non-central chi-square distribution is also provided as a special case of our
unified cdf result.Comment: 2 pages, to be published in the IEEE Transactions on Vehicular
Technology as a Correspondenc
A geometric proof of the equality between entanglement and edge spectra
The bulk-edge correspondence for topological quantum liquids states that the
spectrum of the reduced density matrix of a large subregion reproduces the
thermal spectrum of a physical edge. This correspondence suggests an intricate
connection between ground state entanglement and physical edge dynamics. We
give a simple geometric proof of the bulk-edge correspondence for a wide
variety of physical systems. Our unified proof relies on geometric techniques
available in Lorentz invariant and conformally invariant quantum field
theories. These methods were originally developed in part to understand the
physics of black holes, and we now apply them to determine the local structure
of entanglement in quantum many-body systems.Comment: 7 pages, 3 figure
A correspondence principle for steady-state wave problems
A correspondence principle was developed for treating the steady state propagation of waves from sources moving along a plane surface or interface. This new principle allows one to obtain, in a unified manner, explicit solutions for any source velocity. To illustrate the correspondence principle in a particular case, the problem of a load moving at an arbitrary constant velocity along the surface of an elastic half-space is considered
Deep Optical Flow Estimation Via Multi-Scale Correspondence Structure Learning
As an important and challenging problem in computer vision, learning based
optical flow estimation aims to discover the intrinsic correspondence structure
between two adjacent video frames through statistical learning. Therefore, a
key issue to solve in this area is how to effectively model the multi-scale
correspondence structure properties in an adaptive end-to-end learning fashion.
Motivated by this observation, we propose an end-to-end multi-scale
correspondence structure learning (MSCSL) approach for optical flow estimation.
In principle, the proposed MSCSL approach is capable of effectively capturing
the multi-scale inter-image-correlation correspondence structures within a
multi-level feature space from deep learning. Moreover, the proposed MSCSL
approach builds a spatial Conv-GRU neural network model to adaptively model the
intrinsic dependency relationships among these multi-scale correspondence
structures. Finally, the above procedures for correspondence structure learning
and multi-scale dependency modeling are implemented in a unified end-to-end
deep learning framework. Experimental results on several benchmark datasets
demonstrate the effectiveness of the proposed approach.Comment: 7 pages, 3 figures, 2 table
Superconducting and Anti-Ferromagnetic Phases of Spacetime
A correspondence between the theory of High-T superconductivity
and antiferromagnetism, put forward by Zhang and collaborators, and a theory of
gravity arising from symmetry breaking of a gauge field is presented. A
physical correspondence between the order parameters of the unified SC/AF
theory and the generators of the gravitational gauge connection is conjectured.
A preliminary identification of regions of geometry, in solutions of Einstein's
equations describing charged-rotating black holes embedded in deSitter
spacetime, with SC and AF phases is carried out.Comment: 6 pages, no figures, shortened for journal submission, comments
welcome :
- …