Related papers: Invertible Convolution with Symmetric Paddings
Recent advancements in generalized symmetries have drawn significant attention to gapped phases of matter exhibiting novel symmetries, such as noninvertible symmetries. By leveraging the duality transformations, the classification and…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
We present a geometric framework for the inverse design of smart woven fabrics composed of non-uniformly shrinking threads. A sufficiently tight weaving structure imposes strong local criteria on the material deformation and reduces the…
Convolutional networks are successful due to their equivariance/invariance under translations. However, rotatable data such as images, volumes, shapes, or point clouds require processing with equivariance/invariance under rotations in cases…
The X-ray transform on a compact symmetric space M is here inverted by means of an explicit inversion formula. The proof uses the conjugacy of the minimal closed geodesics in M and of the maximally curved totally geodesic spheres in M,…
We study how group symmetry helps improve data efficiency and generalization for end-to-end differentiable planning algorithms when symmetry appears in decision-making tasks. Motivated by equivariant convolution networks, we treat the path…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
Efficient algorithms for computing linear convolutions based on the fast Fourier transform are developed. A hybrid approach is described that combines the conventional practice of explicit dealiasing (explicitly padding the input data with…
Automated symmetry detection is still a difficult task in 2021. However, it has applications in computer vision, and it also plays an important part in understanding art. This paper focuses on aiding the latter by comparing different…
The nonlinear Fourier transform (NFT) decomposes waveforms propagating through optical fiber into nonlinear degrees of freedom, which are preserved during transmission. By encoding information on the nonlinear spectrum, a transmission…
Understanding the mechanisms underlying deep neural networks remains a fundamental challenge in machine learning and computer vision. One promising, yet only preliminarily explored approach, is feature inversion, which attempts to…
We use supersymmetry transformations to design transparent and one-way reflectionless (thus unidirectionally invisible) complex crystals with balanced gain and loss profiles. The scattering coefficients are investigated using the transfer…
Blurring of a photographic image by a wrong focus can be modeled by convolution. Is inversion a possible answer? This paper adds complements to a foregoing paper discussing convolution-inversion of some measures.
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where…
Starting from nonlocal symmetries related to B\"acklund transformation (BT), many interesting results can be obtained. Taking the well known potential KdV (pKdV) equation as an example, a new type of nonlocal symmetry in elegant and compact…
Purpose: Often, the inverse deformation vector field (DVF) is needed together with the corresponding forward DVF in 4D reconstruction and dose calculation, adaptive radiation therapy, and simultaneous deformable registration. This study…
This paper considers the inversion of ill-posed linear operators. To regularise the problem the solution is enforced to lie in a non-convex subset. Theoretical properties for the stable inversion are derived and an iterative algorithm akin…
Designing flat sheets that can be made to deform into 3D shapes is an area of intense research with applications in micromachines, soft robotics, and medical implants. Thus far, such sheets were designed to adopt a single target shape.…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…