12,778 research outputs found
Ad-nilpotent ideals and The Shi arrangement
We extend the Shi bijection from the Borel subalgebra case to parabolic
subalgebras. In the process, the -deleted Shi arrangement
naturally emerges. This arrangement interpolates between the Coxeter
arrangement and the Shi arrangement , and breaks
the symmetry of in a certain symmetrical way. Among other
things, we determine the characteristic polynomial
of explicitly for and . More generally, let
be an arbitrary arrangement between and
. Armstrong and Rhoades recently gave a formula for
for . Inspired by their result, we obtain
formulae for for , and .Comment: The third version, quasi-antichains are shown to be in bijection with
elements of L(Cox). arXiv admin note: text overlap with arXiv:1009.1655 by
other author
Modulating Image Restoration with Continual Levels via Adaptive Feature Modification Layers
In image restoration tasks, like denoising and super resolution, continual
modulation of restoration levels is of great importance for real-world
applications, but has failed most of existing deep learning based image
restoration methods. Learning from discrete and fixed restoration levels, deep
models cannot be easily generalized to data of continuous and unseen levels.
This topic is rarely touched in literature, due to the difficulty of modulating
well-trained models with certain hyper-parameters. We make a step forward by
proposing a unified CNN framework that consists of few additional parameters
than a single-level model yet could handle arbitrary restoration levels between
a start and an end level. The additional module, namely AdaFM layer, performs
channel-wise feature modification, and can adapt a model to another restoration
level with high accuracy. By simply tweaking an interpolation coefficient, the
intermediate model - AdaFM-Net could generate smooth and continuous restoration
effects without artifacts. Extensive experiments on three image restoration
tasks demonstrate the effectiveness of both model training and modulation
testing. Besides, we carefully investigate the properties of AdaFM layers,
providing a detailed guidance on the usage of the proposed method.Comment: Accepted by CVPR 2019 (oral); code is available:
https://github.com/hejingwenhejingwen/AdaF
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